
Book .IS 

I <Hk 
GopightN _:_ 



COPYRIGHT DEPOSIT. 




Laboratory table, shown in isometric projection. 
Length, 6 ft. ; width, 31 ft. ; height of top, 3 ft. 
Height of cross-bar above top, 3 ft. 4 in. 



LABORATORY EXERCISES 



IN 



PHYSIOS 



FOR SECONDARY SCHOOLS 



BY 

GEORGE R. TWISS 

THE CENTRAL HIGH SCHOOL, CLEVELAND 



REVISED EDITION 



CHICAGO 

SCOTT, FORESMAN AND COMPANY 

1906 



LIBRARY of CONGRESS 




Two Oeples Received 




OCT 17 1906 




A Cepyrlfht Entry 


Tl 


iqofc 



Copyright, 1902 

BY 

THE MACMILLAN COMPANY 



Copyright, 1906 

BY 

SCOTT, FORESMAN AND COMPANY 



PKEFACE 

This book presents fifty-seven exercises and fifty- 
six supplementary or optional problems for the lab- 
oratory, and affords ample variety for a selection 
by the teacher of from thirty to forty experiments 
for a year's course. These are designed to be used 
in conjunction with text-book lessons and class-room 
demonstration. 

Adequate material will be found here for fully 
supplementing any good class book; but the manual 
is in especially close harmony with the spirit and 
method of the "Mann and Twiss Physics.'** The 
authors of that book recommend the manual for use 
with their text. 

A prominent feature of both the text-book and 
the manual is the subordination of manipulation to 
thought processes. 

The Author is strongly in sympathy with the new 
movement which is now gathering force throughout 
this country and Europe, and which has for its aim 
the recovery of some of the enthusiasm and vitality 
of interest which characterized the study of physics 
a generation ago when it went by the name of 
Natural Philosophy. We ought not to lose sight of 
the fact that our main work is to train up sane and 

*Physic8. By ('. R. Mann and G. R. Twiss. Chicago, Scott, 
Foresman and Co. 1905. 

v 



VI PREFACE 

competent men a ad women for the ordinary voca- 
tions of life, and not to make physicists. 

Attention is respectfully directed to the following 
features which it is believed will especially commend 
this manual to thoughtful teachers: 

1. By the choice of subject-matter and method 
of presentation the attention of the student is guided 
toward the observation of important phenomena and 
the interpretation of their relations to one another, 
rather than toward the peculiarities of instruments 
of precision or the niceties of exact measurement. 

2. A majority of the exercises, however, do 
require measurements of some care, and they all 
demand attentive observation and clear thinking; 
but measurements are emphasized, not as an end in 
themselves, but rather as a means of finding out 
how phenomena are related to one another. 

3. The experiments are simple, interesting, and 
workable, and represent fundamental principles which 
the student may find in operation all about him. 

4. The apparatus required is all very simple and 
inexpensive, and no specially designed or unusual 
pieces are demanded. Nearly all the experiments 
may be made with such equipment as is already 
possessed by most school laboratories. With the 
exception of a very few pieces, the entire equipment 
may be ' ' home-made" by the teacher and some of the 
boys who are handy with tools: in fact, a great part 
of the laboratory apparatus in the Central High 
School at Cleveland has been so made. 

5. The book contains a system of suggestions for 



PREFACE Vll 

the making of laboratory notes which in the course 
of the year will train the student to arrange his 
record methodically and to devise tabular forms 
for himself. In a number of cases such forms are 
printed in the book because these particular forms 
are found to be more suggestive to the student in 
reaching his conclusions and more convenient for 
quick inspection by the teacher than any that he is 
likely to devise for himself. 

6. Throughout the work the student is aided by 
suggestions and pointed questions which clear the 
difficult portions of his path so that he can proceed 
alone where it is less difficult. 

7. The book has grown into its present form out 
of the Author's actual experience of twenty years in 
teaching physics to high school scholars of both sexes 
and all grades of natural ability. The directions 
for experimenting have gone through many revisions 
and thus they have been made so clear and explicit that 
if the student asks what he is to do or how he is to 
do it, he may be told to look in his manual for the 
answer. By a careful re-reading he will almost 
invariably find the means of answering his own 
question. This teaches him to rely on his own 
resources, rather than to lean on the teacher. 

8. Since the teacher is thus freed from the weary- 
ing and profitless repetition of details, he will have 
more time and energy left for the broader and more 
important work of teaching fundamental principles 
and inculcating correct habits of thought and 
expression. 



Vlll PREFACE 

Grateful acknowledgment is hereby tendered to 

Prof. Frank Perkins Whitman, of Western 

Reserve University, and to Mr. Franklin Turner 

Jones, of the University School, Cleveland, for 

their thorough and critical reviews of the manu- 

manuscript and proof sheets of the first edition. 

The Author also hereby extends his hearty thanks 

to Prof. Charles Riborg Mann, of the University of 

Chicago, who has been his active adviser in the 

preparation of the present revised edition, and to 

whose wise suggestions much of the improvement 

is due. 

George Ransom Twiss. 

Cleveland, August 27, 1906. 



CONTENTS 

Introduction. To the Student 

PACJE 

The Laboratory xv 

Abbreviations Used in This Book xvii 

Text Book References . . . . . . xviii 

CHAPTER I 

Mechanics of Solids 

EXERCISE 

1. Experiment. Timing a Pendulum 1 

2. Experiment. Study of a Falling Body 4 

3. Graphical Problem. Accelerated Motion. Velocity- 

Time 8 

4. Graphical Problem. Accelerated Motion. Distance- 

Time 11 

5. Experiment. Comparison of Masses by the Acceler- 

ation Method 13 

6. Experiment. Density of a Regular Solid 18 

7. Experiment. Elasticity of a Helical Spring .... 19 

8. Graphical Problem. Stretching Force — Elongation . 22 

9. Experiment. Pulleys. Mechanical Advantages and 

Efficiency 23 

10. Experiment. Concurrent Forces. Parallelogram. 

Vectors 27 

11. Experiment. Inclined Plane Work 34 

Optional Problems, (a) Mechanical Advantage . 37 

(b) Effect of Changing Slope 37 

(c) Resolving the Weight into Components . . 37 

(d) Closed Vector Triangle for Equilibrium . . 38 

(e) Law of Mechanics Derived 3S 

(/) Efficiency of the Inclined Plane 3S 

12. Experiment. Simple Strut and Tie. Resolution of 

Forces 39 

Optional Problem. Test by Closed Vector Triangle 42 
ix 



X CONTENTS 

EXERCISE PAGE 

13. Experiment. Levers. Moments 42 

Optional Problems, (a) Force at Fulcrum ... 44 

(b) Mechanical Advantage 45 

(c) Fulcrum at One End 45 

(d) Efficiencies 45 

(e) Application of the Law of Mechanics ... 46 

14. Experiment (Alternative). Wheel and Axle Moments 46 

Optional Problems, (a) Efficiency 48 

(b) Experiments with a Dissected Clock ... 48 

15. Experiment, Equilibrium of Parallel Forces ... 48 

16. Experiment. Center of Mass 52 

17. Experiment. Equilibrant of Parallel Forces. Effect 

of the Weight of the Bar 54 

Optional Problems, (a) Moments about Any Axis 56 

(b) Weight of the Bar Unknown 57 

(c) Center of Mass Unknown 57 

(d) Principle of the Steelyards . 57 

18. Experiment. Phenomena of the Pendulum .... 57 

Part A. Relation of Period to Length and Ampli- 
tude 57 

Part B. Acceleration of Gravity 61 

Optional Problems, (a) Period — Length Graph . 62 

(b) Mass and Period 62 

CHAPTER II 
Fluids 

19. Experiment. Density of Water 64 

20. Experiment. Pressure in a Liquid caused by its 

W x eight 65 

Optional Problems, (a) Relation of Pressure to 

Direction 68 

(b) Pressure in Water Pipes on Different Floors 68 

(c) Comparison of Measured Pressures with Cal- 

culated Weights 68 

21. Experiment. The Principle of Archimedes .... 69 

Optional Problem, (a) Special Case of a Floating 

Body 70 

(b) Displacement and Carrying Power of a Toy 

Boat 71 



CONTENTS Xl 

EXERCISE PAGE 

22. Experiment. Density by Submersion ...... 71 

Part A. Of a Solid 71 

Part B. Of a Liquid 73 

23. Experiment. Density by Flotation 76 

Part A. Of a Solid 77 

Part B. Of a Liquid 79 

24. Experiment. Density by Hare's Method of Balanc- 

ing Columns Supported by Atmospheric Pressure 82 

25. Experiment. Calibration and Use of a Lactometer . 86 

Optional Problems, (a) Milk Test 88 

(b) Babcock Cream Test 89 

26. Experiment. Construction and Use of Pumps ... 90 

Optional Problems, (a) "Suction" 92 

(6) Force Pump • 93 

(c) Siphon 93 

27. Experiment. Boyle's Law 94 

Part A. Verification 94 

Part B. Optional Problem. Pressure-Volume 

Graph 97 



CHAPTER III 
Heat 

28. Experiment. Changes of Temperature and of State 98 

Optional Problems, (a) Boiling Point Error . . 102 

(b) Melting Point of Tallow or Beeswax ... 103 

(c) Boiling Point of Alcohol 103 

(d) Boiling Point by the Vapor Pressure Method 103 

(e) Effect of Dissolved Salts on the Boiling Point 104 
(/) Effect of Surface of Containing Vessel . . 104 
(g) Effect of Pressure on the Melting Point of Ice 104 

29. Experiment. Dew Point and Relative Humidity . 104 

Optional Problems, (a) Humidity at Home . . 107 

(6) Humidity out of Doors 107 

30. Experiment. Specific Heat of a Metal 108 

81. Experiment. Heat of Melting of Ice 113 

32. Experiment. Heat of Vaporization of Water ... 117 



Xll CONTENTS 

CHAPTER IV 

Electricity and Magnetism 

EXERCISE PAGE 

33. Experiment. Lines of Force about a Bar-Magnet . 122 

34. Experiment. Lines of Force about a Current . . 126 

35. Experiment. Short-Distance Telegraph 129 

36. Experiment. Long-Distance Telegraph 132 

37. Experiment. Electric Bells and Domestic Wiring . 135 

Optional Problems, (a) Electric Gas Lighter and 

Spark Coil 137 

(6) Bells in Series 137 

(c) Bells in Multiple Arc 137 

(d) Best Arrangement of Cells 137 

(e) Effect of Resistance on Bells in Multiple Arc 137 

38. Experiment. Induced Currents 138 

Optional Problem, (a) Reversibility of Dynamo 

and Motor 141 

(b) Dissected Dynamo. Shunt and Series Wind- 
ing 141 

39. Experiment. Electrical Resistance. The Wheat- 

stone Bridge 141 

Optional Problems, (a) Resistance and Power by 
Ammeter and Voltmeter. "Hot" and 

"Cold" Resistance of a Glow Lamp . . . 146 

(b) "Hot" and "Cold" Resistance of an Electric 

Heater 146 

(c) Relation of Resistance to Length 146 

(d) Resistance and Sectional Area 146 

(e) Resistance and Material 147 

(/) Resistivity 147 

40. Experiment. Simple Voltaic Cell 147 

41. Experiment. Electro-Plating 151 

Optional Problems, (a) Storage Battery .... 155 
{b) Current Strength. Copper Voltameter. Cali- 
bration of an Ammeter or Galvanometer 157 

CHAPTER V 
Sound 

42. Experiment. Velocity of Sound in Open Air ... 158 

43. Experiment. Rating a Tuning-Fork 161 



CONTENTS xiii 

EXERCISE PAGE 

44. Experiment. Wave Length by Resonance .... 165 

45. Experiment. Cause of Overtones 168 

46. Experiment. Vibrating Strings — Length 173 

47. Experiment. Vibrating Strings — Tension ..... 176 

48. Experiment. Vibrating Strings — Sectional Area . . 178 

CHAPTER VI 
Light 

49. Experiment. Law of Inverse Squares. Bunsen's 

Photometer 180 

50. Experiment. Law of Inverse Squares. Rumford's 

Photometer 184 

Optional Problem. Shadow Method 188 

51. Experiment. Candle Power of a Lamp 188 

52. Experiment. Law of Reflection 189 

53. Experiment. Image in a Mirror 192 

54. Experiment. Index of Refraction 194 

55. Experiment. Focal Length of a Lens. Use of Spec- 

tacles 198 

56. Experiment. Conjugate Foci 201 

Part A. Relations of Image and Object. Appli- 
cations to Optical Instruments. . . . 202 
Optional Problem. Image Size and Distance . 203 
Part B. Conjugate Focal Distances 204 

57. Experiment. Study of Spectra 205 

CHAPTER VII 

Appendices 

A. Errors and Significant Figures — 

1 . Errors — Experimental Errors. Mistakes or Blun- 

ders. Errors of Observation. Instrumental 
Errors. Error of a Single Observation ... 211 

2. Mean of a Series of Observations. Its Probability 211 

3. Significant Figures 211 

4. Rules for Precision of Numerical Statement. Fig- 

ures That Are to Be Discarded. The Last 
Figure Retained. Number of Significant Fig- 
ures to Be Retained 212 



Xiv CONTENTS 

PAGE 

B. Methods of Measuring Length — 

1. Use of a Rule. Estimating Tenths of a Scale 

Division ■. 213 

2. Use of Squared Blocks 213 

3. Use of Calipers 213 

4. Use of the Vernier Slide Caliper 214 

5. Use of the Micrometer Screw Caliper 215 

6. To Measure the Diameter of a Wire 216 

C. Methods of Determining Areas and Volumes — 

1. Plane and Solid Geometrical Figures 217 

2. Measuring Volume with a Graduate 217 

D. Methods of Measuring Mass — 

1. The Equal Arm Balance 218 

2. The Trip Scales 220 

3. The Jolly Balance 220 

4. A Rubber Band Dynometer 221 

E. Barometer 222 

F. Suggestions Concerning Apparatus . 223 

G. Pressure and Temperature of Water Vapor .... 229 

H. Soft Wax. Cements. Soldering 229 

I. Reference Books for Teachers 230 



TO THE STUDENT 

The Laboratory is the place to test and apply what 
you learn in the class room. The value of the train- 
ing that you will get out of it will depend on the 
faithfulness with which you carrry out the instruc- 
tions of your teacher and of this book. 

Punctuality. — Begin and stop your work promptly 
at the proper signals. 

Attention. — Keep your attention fixed on the work 
in hand. Listen carefully to every suggestion of 
the instructor. Never speak except in a whisper or 
low undertone. 

Order. — Preserve an orderly arrangement of ap- 
paratus while at work. See that things are always 
in the positions where they can be used most readily 
and conveniently. 

Neatness. — If the apparatus or the table becomes 
dusty or wet, dry or clean it immediately. If you 
find anything at your table in bad condition report 
it to the teacher before beginning work. Do not 
leave papers or litter on floor or tables. Deposit 
them in the receptacles provided for them. 

Explanations. — Do not ask questions of your fel- 
low students unless you are directed to consult with 
them. Do not ask a question of the teacher until 
you have looked carefully for the answer in your 



xvi TO THE STUDENT 

laboratory manual and text-book and failed to find 
it there. 

Sinks. — Never throw anything into the sinks ex- 
cepting water. 

Preparation. — Study carefully each Exercise before 
the laboratory hour. Do not try to commit direc- 
tions to memory, but think'out everything they tell 
you to do. Try to comprehend the plan of the 
work, and picture to yourself just how you will carry 
it through. Where your previous instruction has 
prepared you for it, try also to think out the kind of 
results you may reasonably look for and the conclu- 
sions you may possibly reach. 

Prepare the page upon which your notes are to be 
taken. Have tabular forms ruled and spaces allotted 
for the different kinds of notes. 

Carefulness. — Keep the plan and purpose of the 
experiment constantly in mind. Observe keenly 
everything that happens during your experiment, 
and when measurements are to be made get the values 
as accurately as you can with the apparatus pro- 
vided. Record phenomena and numerical data just 
when they are observed. Record exactly what you 
observe, not what you think you ought to observe. 
You cannot acquire the scientific spirit or get the 
value of the laboratory training unless you are abso- 
lutely honest with your own intellect. 

Note Books. — Never make notes or calculations 
on loose paper. Keep them all in your note 
book. 

Do not erase numerical data. Enclose rejected 



TO THE STUDENT xvii 

matter in brackets and write "rejected" at the side 
of it. 

Express fractions and ratios decimally. Do not 
crowd the notes together. Arrange them systemat- 
ically and leave generous spaces between different 
parts of the subject-matter. Label calculations and 
diagrams, and make the paragraph headings promi- 
nent. In other matters pertaining to your notes, 
follow carefully the directions given you by the 
teacher. 

Borrowing. — Xever borrow a note book from an- 
other student, or lend your own without permission 
from the teacher. Xever take apparatus from one 
place to another in the laboratory unless so directed. 



ABBREVIATIONS USED IN THIS BOOK 

Art. 

A. 

B. 

Cf. 

cc. 

cm. 

cm. 2 

cm. 3 

cm 

sec 

cm 

sec 2 

D 

Ex. 

F.,f. 

gm. gram 



Article, paragraph. 


g. 


the acceleration of a free 


Acceleration. 




ly falling body. 


Barometric reading. 


h. 


height. 


Compare. 


K 


any constant. 


cubic centimeter. 


1 


length or distance. 


centimeter. 


M,m 


mass. 


square centimeter. 


m. 


meter. 


cubic centimeter. 


mm. 


millimeter. 


centimeter per second. 


R,r 


radius. 




sec. 


second. 


— per second, 
sec ^ 


T,t 


time, period. 


density. 


V 


velocity. 


Exercise. 


V 


volume. 


force. 


W,wt 


. weight. 



xvni TO THE STUDENT 

TEXT-BOOK REFERENCES 

The text- books referred to by paragraph numbers 
at the beginning of each exercise are named below: 

M & T . Physics. Mann & Twiss. Scott, Foresman and Co. 

A . . . . School Physics. Avery. Butler, Sheldon & Co. 

C . . . . Elements of Physics. Crew. The Macmillan Com- 
pany. 

C & . . High School Physics. Carhart & Chute. Allyn & 
Bacon. 

GE . . Elements of Physics. Gage. Ginn & Co. 

GP . . . Principles of Physics. Gage. Ginn & Co. 

H .... A Brief Course in Physics. Hoadley. American 
Book Company. 

H & W . Elements of Physics. Henderson & Woodhull. D. 
Applet on & Co. 

J . . . . Heat, Light and Sound. Jones, D. E. The Mac- 
millan Company. 

J & J . . Elementary Electricity and Magnetism. D. C. & 
J. P. Jackson. The Macmillan Company. 

L . . . . Elementary Mechanics. Lodge. The Macmillan 
Company. 

T . . . . Elementary Lessons in Electricity and Magnetism. 
Thompson. The Macmillan Company. 

W & H . A Text-Book of Physics. Wentworth & Hill. Ginn 
&Co. 



Laboratory Exercises in Physics 

CHAPTER I 
MECHANICS OF SOLIDS 

Exercise Number 1 
timing a pendulum 

References 

C17 H 17 M&T2 

GP 3 H & W 39 

The Purpose of the experiment is to determine the 
time of oscillation of a pendulum, in order to use it 
as a time measurer in experiments with freely falling 
bodies. 

The Apparatus consists of a laboratory clock or 
watch, and the pendulum (P Fig. 1, p. 2), consist- 
ing of a flat strip of wood with a pair of movable 
weights for a bob. It is suspended from a firm sup- 
port by means of a strip of flexible leather. 

Operations. — (a) One observer, A, sees to it that 

the second hand of the time piece is set so as to come 

to zero at the instant when the minute hand marks 

an even minute. Another observer, B, draws the 

pendulum aside through a small arc. A notes the 

hour, and when the second hand is nearly at zero, 

i 



LABORATORY EXERCISES IN PHYSICS 



says "Keady!" Just when the second hand reaches 
zero, he says "Now!" and B instantly lets go the 

pendulum, being 
very careful not 
to push it. He 
then counts the 
double swings of 
^ the pendulum, 
beginning with 
"One" when the 
pendulum com- 
pletes its first dou- 
ble swing, or round 
trip. A, mean- 
while watches the 
time, and notes the 
minute and second 




Fig. 1. 



when he 
"Now." 

(5) When 
time agreed 
say 100 sec. 
Eeady." B 



said 

the 
on, 
has 
then 



nearly elapsed he again says 
follows the motion of the pendulum with his hand, 
keeping in time with its rhythmic motion, so he can 
stop it just where it is when A gives the word. 
When the 100th second is completed, A says 
"Now!" and B stops the pendulum. He then states 
the number of single oscillations and the decimal 
fraction of a single oscillation made by the pendu- 
lum between the instants of starting and stopping. 



MECHANICS OF SOLIDS 



By a single oscillation is meant a swing from one 
extreme position to the other, as distinguished from 
a complete vibration, or swing to and fro. A and 
B should exchange places after each trial. 

A more accurate, but somewhat more difficult method is to 
observe the time, first when the pendulum passes its lowest 
point, and again when it passes this point in the same direction 
after say 30 complete vibrations. In this case the fractional 
parts .of a second must be estimated, and expressed to tenths. 

If a stop watch is provided, it affords the simplest and most 
accurate means of measuring short time intervals for begin- 
ners, as it always starts at zero and stops at an even fifth of a 
second. 

Data and Calculations. — Calculations should be 
entered in full on one of the left hand pages of the 
note book, and the final results tabulated as sug- 
gested by the annexed ruled form. In the calcula- 
tions retain four figures (cf . Appendix A, Art. 3 and 
4). A set of these observations should be made 
with the weights at (#), another set with them at (J), 
and a third set with them at (c). 

Observations made by ....and 



Seconds 


Oscillations 


Time of 
Oscillation 






Sec. 






" 




" 


Mean time, Weights at (c 


l) 








" 






" 



Errors. — State briefly the sources from which errors. 



4: LABORATORY EXERCISES IN PHYSICS 

personal and instrumental, are likely to arise. (Cf. 
Appendix A, Art. 1.) 

Lessons. — This exercise is preliminary to Exercise 
2; but incidentally the student may learn several 
things in connection with the phenomena which he 
has had opportunity to observe. Let each one an- 
swer in his note book, in complete sentences, the 
following questions: 

(a) Are the oscillations made in equal times even 
though they are made through unequal arcs, provided 
the arcs are small ? 

(5) At what position does the pendulum bob have 
its greatest velocity? What velocity does it have at 
either end of the swing ? 

(c) What fraction of the time of oscillation is re- 
quired in going from either extreme position to the 
middle ? 

(d) If a clock gains or loses time, what may be 
done with its pendulum in order to regulate it ? 

Exercise Number 2 

study of a falling body 

References 

A 18, 19, 101-108 GE 5, 10-13 H & W 68-76 

C 9, 25-29, 81-86 GP 2, 10-14 L 7-12 

C & C 8, 31-34 H 12, 78-84 M & T 2-20 

W&H 10, 166-171 

The Purpose is to find out what distances a body 
traverses when it starts from rest and falls for dif- 
ferent time intervals, and to determine the acceler- 
ation. 



MECHANICS OF SOLIDS 5 

The Apparatus (cf. Appendix F, Art. 1) consists 
of the pendulum that was rated in Exercise 1, a 
heavy ball, a meter stick, and a stick of bicycle 
graphite. 

Operations. — (a) A strip of manila paper of the 
same length and width as the wooden rod of the 
pendulum, is attached to the rod with thumb tacks 
or soft wax (cf. Appendix H, Art. 1). The ball is 
coated with graphite, and hooked into a loop at one 
end of a long cotton string, which is then passed 
over the two hooks d and e, and fastened in the 
binding post f at such a point that the ball hangs 
with its center just at the upper end of the pendulum 
rod, while the pendulum is drawn back bv the string 
as shown in Fig. 1, p. 2. 

Before thus arranging the apparatus, the hook e 
should have been adjusted in such a position that 
the ball, when hanging as a plumb-bob, will just 
touch the face of the rod at any point of its length, 
while the latter is hanging freely in its vertical 
position. 

(b) After seeing that the pendulum and the ball are 
perfectly motionless, the observer burns the string 
with a match. This releases the ball and pendulum 
at the same instant; and the pendulum, just as it 
completes a half oscillation, strikes the ball, so as to 
print a black spot on the paper. If the weights 
were at #, mark this spot a v In exactly the same 
way, make one or two other trials, and mark the 
spots & 2 , « 3 , etc. 

(c) If time permits, another set of trials should be 



6 



LABORATORY EXERCISES IN PHYSICS 



made with the weights at Z>, and a third set with 
them at c. The spots should be marked b v Z> 2 , c v c 2 , etc. 

(d) The paper strip is now removed and laid flat 
on the table. The distance from each of the spots 
to the upper end of the paper is to be measured in 
centimeters to the tenth of acm. (and also, if the 
instructor so directs, in inches to the sixteenth of an 
inch. In this case the results should be reduced to 
feet and hundredths of a foot). In measuring, the 
meter stick should be set on edge, so that the scale 
divisions are in contact with the paper, and the ob- 
server should sight along the division line of the 
scale, where the reading is taken, so as to avoid the 
error called parallax. Care should be taken also 
that the measurement is made along a straight line. 

Data. — Place the results in a neatly ruled tabular 
form, as suggested below. 

Numerical Data 
Observations made by 



Position of weights 


a 


b 


c 


Time (of single oscillation) = t 








Distance, 1st trial 






2d trial 








3d trial 








" mean = Z 








Acceleration = -5 








Mean value of the acceleration from a, b, and c, 




Per cent error 





MECHANICS OF SOLIDS T 

Calculations. — The average velocity is the distance 
/ divided by the time t ; the final velocity is twice 

the average velocity, or — ; and the acceleration, 

o 

a= i.e. the change of velocity — . divided by the 
t t 

time t. 

Sources of Error. — When the pendulum bob is in 
its lowest position, that in which it would come to 
rest, it is assumed in the experiment that the face of 
the rod is in the vertical line along which the ball 
falls. If this is not true, the paper will meet the 
ball either before or after the instant when the pen- 
dulum has completed a half oscillation, and the dis- 
tance measured will be that fallen in a less or a greater 
time than that assumed. A similar error will be 
caused if the ball is swinging toward or from the 
pendulum at the time of beginning its fall. What 
other sources of error can you name ? 

Inferences. — {a) Are the values of the acceleration 
nearly enough equal so that we may think the differ- 
ences due to experimental errors ? 

(b) If so, may you say that, so far as your experi- 
ments go, the acceleration of the falling ball is con- 
stant ? 

(c) The acceleration being the ratio of change of 
velocity to time, and being constant, may we say 
that the changes of velocity of a freely falling body 
are proportional to the times of falling ? 

(d) Since also the acceleration is twice the ratio of 
the distance fallen to the square of the corresponding 



8 



LABORATORY EXERCISES IN PHYSICS 



time, if this acceleration is constant, may we say 
that when a falling body starts from rest, and falls for 
different time intervals, the distances traversed are 
directly proportional to the squares of the times of 
falling ? 

Exercise Number 3 



GRAPHICAL, REPRESENTATION OF ACCELERATED 
MOTION. VELOCITY-TIME 

References 

M & T 4, 5 

The Purpose of this exercise is to find out what 

kind of diagram 
will represent the 
way in which the 
velocity varies with 
the time in the 
case of the falling 
body of Exercise 2. 
Operations. — 
Near the lower left 
hand corner of the 
note book page, 
or of a sheet of 
squared paper, 
choose a point O 
(Fig. 2) at the in- 
X tersection of two 
Fig.2. lines. ' This point 

will be called the origin. From the origin, draw two 




MECHANICS OF SOLIDS 9 

heavy lines, OX horizontal, and OY vertical. La- 
bel OX "Axis of Abscissas. Times," and OY 
"Axis of Ordinates. Velocities." Below OX write 
"Scale, 1 cm. = 0.15 sec," and at the left of OY 
write "Velocities. Scale 1 cm. = lOO^;." 

(5) The times are to be represented by distances 
from OY measured in the direction OX; and the 
velocities by distances from OX measured in the 
direction of OY. The scale according to which the 
quantities are represented must be of such a magni- 
tude that the diagram will be of convenient size for 
the page. 

(c) From your data for Exercise 2, take the values 
of £, divide each by the scale number (0.15 in this 
case), to find the number of cm. by which each value 
of t is to be represented in the diagram. Similarly, 
for the corresponding velocities, divide each by 100. 
Enter the times, the corresponding velocities, and 
the numbers that are to represent them in a neat 
tabular form near the diagram. 

(d) The first point of the diagram is that which 
will represent the instant of starting. This is the 
instant from which we begin to count both time and 
velocity, so the time elapsed is zero, and the veloc- 
ity gained since the instant of starting is also zero. 
Evidently the point O represents both time and ve- 
locity at this instant, and is therefore the first point 
of the required diagram. 

(e) For the next point, lay off from O on OX the 
number of cm. that is to represent the smallest value 
of t\ and mark the point x v Similarly, lay off from 



1 LABOR ATOR Y EXERCISES IN PHYSICS 

on OY the number of cm. that is to represent the 
velocity gained during this time, and mark this 
point y . From a? draw a vertical dotted line, and 
from y x a horizontal dotted line intersecting the ver- 
tical at a point p ± . This point represents the first time 
of falling, since its distance ^rom OY is propor- 
tional to that time ; and it also represents the velocity 
gained during that time, because its distance from 
OX is proportional to that velocity. 

(f) The point j? 2 , representing the next smallest 
time of falling and the corresponding velocity, is 
found in exactly the same way. Similarly for the 
points p 3 , p 4 , etc. representing other times and the 
corresponding velocities. The abscissas and ordi- 
nates are always to be measured from 0/ and the 
times and corresponding velocities are all to be the 
total values from the instant of starting. 

(g) The diagram, or graph as it is called, is com- 
pleted by drawing the straight line, or the smooth 
curve (whichever it may be) that most nearly passes 
through all the points (9, p v p 2 , etc. To look well, 
this line should be drawn with a draftsman's pen and 
red ink. If the line is curved, the pen should be 
guided by a "French curve" or a piece of whalebone. 

(A) Label the graph, "Freely Falling Body. Re- 
lation of Changes in Telocity to Corresponding 
Times." The distances 0x v 0x 2 , etc. are the ab- 
scissas, and the distances x 1 p 1 — Oy v x 2 p 2 = Oy 2 , 
etc. are the ordinates, of the points p x p 2 , etc. The 
abscissa and ordinate of a point are called its co-or- 
dinates. 



MECHANICS OF SOLIDS 11 

Inferences. — Answer in complete sentences, (a) 
Is the graph just drawn a straight line ? If it is 
straight, can you prove by similar triangles that the 
ordinates are proportional to the corresponding ab- 
scissas ? 

(b) If so, since the abscissas represent times and 
the ordinates the corresponding gains in velocity, 
what relation does the straight line graph show exists 
between the velocities gained and the times in which 
they were gained ? 

(c) Does the uniform slope of this velocity-time 
graph mean that the body whose motion it represents 
is gaining velocity at a constant rate, i.e. that its 
acceleration is constant ? 



Exercise Number 4 

distance -time graph for uniformly acceler- 
ated motion 

References 

M &T4, 5, 12, 13 

The Purpose is to find out what kind of graph will 
represent the relation between the times of falling 
and the total distances traversed in those times, in 
the case of the falling ball of Exercise 2. 

Operations. — Proceed exactly as in the preceding 
exercise, except that the ordinates are now to rep- 
resent the distances traversed in the various times 
instead of the velocities gained. The scale for the 
times may be 1 cm. = 0.1 sec, and the scale for 
the distances, 1 cm. = 20 cm. 



12 LABORATORY EXERCISES IN PHYSICS 

Inferences. — (a) Does the slope of the graph in- 
crease, decrease, or remain constant ? (b) The slope 
now represents the velocity, not the acceleration {i.e. 
the ratio of change of distance to time instead of 
the ratio of change of velocity to time). Does the 
slope show that this velocity is constant, or vari- 
able ? Increasing, or decreasing ? 

Note. — This graph belongs to a class of curves called 
parabolas. The characteristic peculiarity of a parabola is 
that the abscissas vary in direct proportion to the squares 
of the ordinates, or vice versa. If we get such a curve from 
the data of an experiment, we may infer from it that one of 
the quantities represented by it varies as the square of the 
other. In this case, the distance varies as the square of the 
time, as we found by inspection of the tabulated data of 
Exercise 2. If we find, as in this case, that a graph appears 
to be a parabola and are not sure that it is one, we cannot 
infer with certainty that the ordinates are proportional to the 
squares of the abscissas {i.e. as in this case of the falling body 
that the lengths are directly proportional to the squares of 
the times). A quick and easy way of testing the matter is to 
plot a new graph, with the same ordinates but with the former 
abscissas squared. ( In this case represent the values of I by 
the ordinates as before and the squares of the corresponding 
values of t by the abscissas.) If the resulting graph is a straight 
line we may then be sure that the relation represented by the 
first graph is what we supposed it to be, i.e. that the ordinates 
are proportional to the squares of the abscissas (or in this case 
that the distances are proportional to the squares of the times) . 
A little thought about the use of the graphical method will con- 
vince the student that it is very useful in discovering what 
relation exists between the values of two quantities (like I and 
t in Exercise 1) , one of which changes in value whenever the 
other is changed. Thus a graph may tell us whether the 
distances are directly proportional to the times, or directiy 
proportional to the squares of the times, or inversely propor- 
tional to the times, and so on. 



MECHANICS OF SOLIDS 13 



Exercise Number 5 
comparison of masses by the acceleration 

METHOD 
Xote. — The experience gained in this experiment is very 
useful for fixing in mind the relations of force, mass and accel- 
eration; but in the case of many pupils it requires considerable 
practice before good results can be obtained. In case the 
teacher thinks best to omit it from the laboratory course, 
the author advises giving it, at least roughly, at the demon- 
stration table. 

References 

A 27, 11, 60-66 GP 9-11, 29,32-38, 41, 44, 63, 78 

C 2-7, 14, 16-21, 25-29, 33, 34, H 35-40, 44-46 

45, 50, 51, 54-56, 58, 63 H & W 62-65, 67 

C & C 30-34, 39-44 L 1-12, 29-36, 41-49 

GE 10-12, 22, 26, 27, 31-34 M & T 9, 22-28, 31 
W & H 16, 17, 161, 168, 174, 178-183 

Purpose. — The purpose of this exercise is to apply 
equal forces to two masses for equal time intervals, 
and to determine whether the greater or smaller mass 
acquires the greater velocity ; to determine whether 
their masses are equal if with forces equal they re- 
ceive equal accelerations ; and to learn what degree 
of accuracy is possible in adjusting masses to equality 
by this method. 

Apparatus. — ■ The apparatus is as follows: Two 
cars, provided with hooks or screws at front and 
rear ; two rubber bands or strips of pure gum tubing, 
r, r v of equal lengths and elastic forces, and with 
loops at their ends; two smooth boards, B, B v with 



14 



LABORATORY EXERCISES IN PHYSICS 



hooks near their ends ; a supply of 
lead weights or of iron nuts and 
nails ; a spring balance, or a pair 
of trip scales and weights ; a small 
S-shaped hook of stiff wire. 

Operations. — (a) By means of 
the S-hook join the two bands and 
stretch them over a measuring stick, 
so that the ends of the bands are at 
the ends of the stick. If their 
elastic forces are equal when they 
are equally stretched, the junction 
will be at the middle of the rule. 
Why ? If the S-hook does not lie 
exactly over the middle division, the 
stronger band must be trimmed 
along its edge until the hook remains 
in the right position. 

(5) Place a load of nails and nuts 
in one car, and of nails only in the 
other ; attach the rubber bands to 
the cars and to one of the pairs of 
hooks in the boards ; draw back the 
cars until the bands are stretched 
far enough to give the cars moderate 
velocities. Now secure the cars by 
a piece of twine, looped upon the 
two hooks in the backs of the cars 
and passed around the second pair 
of hooks in the boards. 

(V) Adjust the cars so that their 




MECHANICS OF SOLIDS 15 

front edges are in the same line and the bands 
equally stretched. 

(cT) Hold a rule between the cars and the two front 
hooks, and parallel with the line of the front edges of 
the cars, so that the car boxes, but not the wheels, 
will strike the rule about where the rubber bands 
cease to pull. 

{e) With a lighted match, burn the twine between 
the two rear hooks, in order to release both cars at 
the same instant. 

(/) Note which car has the greater mass as in- 
dicated by the velocity which the tension of the rub- 
ber band imparts to it, and, by repeated trials, adjust 
the masses till the cars have equal velocities, which 
will be when they start and arrive at the same in- 
stant. The adjustment should be made by adding, 
say, eight nails at a time to the car of lesser mass. 
When the addition of eight nails causes this car to 
arrive later than the other, remove as many as neces- 
sary of this last eight, — one or two at a time. 

(</) Test the accuracy of the adjustment by de- 
termining the least number of nails which must be 
added, first to one load and then to the other, in order 
to cause a clearly perceptible difference in the time of 
arrival. 

(h) When the adjustment is completed, determine 
the mass of each car and its load by the method of 
weighing, with the trip scales, or in a pail suspended 
on the hook of the spring balance, estimating the 
fractions of scale divisions in tenths. 

(i) If time permits, repeat with different masses. 



16 



LABORATORY EXERCISES IN PHYSICS 



Observations. — (a) When the forces are equal and 
the masses evidently unequal, which mass is given 
the greater velocity ? 

(5) What is the effect, upon the velocity, of in- 
creasing the mass ? 

(c) What is the effect, upon the velocity, of in- 
creasing the force ?. (This can be done by stretching 
the band farther.) 

Data. — Let m == mass of first car and load, w! the 
mass of the second car and load, R and R r the first 
and second readings of the balance, P the mass of 
the pail (to be subtracted from R and R r to obtain 
m and ra'), and n the least amount of additional 
matter (grams) required to cause an observable 
change in velocity. If a trip balance is used, the 
pail will not be needed, and then m and m' are 
obtained directly. The only quantities to be tab- 
ulated will be m, m', and n. 

Numerical Data 



Trials 


R 


/?' 


P 


R- p=m 


Rf-P = m' 


n 


1 














o 














3 















Calculate and record your per cent error. 
Theory. — Let v and v ! be the velocities of the cars, 
t and t f the time intervals during which they travel, 



MECHANICS OF SOLIDS 17 

and F and F r the forces applied; then F= — and 

j?i = V^lL . (Force is measured by the product of 

mass and acceleration.) But F = F f (hypothesis), 

hence — = — — . Also v = v f and t = t f (because 

the cars start and arrive at the same instants, and 
pass over equal distances). Therefore dividing both 

members by the common factor - or — (which is the 
acceleration) we have m = w! ' • 

Sources of Error. — Some of the most important 
errors result from — 

(a) Parallax and personal equation in reading 
the balances and observing the arrival of the cars. 

(5) Inequality of the forces. The bands should 
be tested frequently and readjusted if necessary. 

(e) Difference in friction of the two cars. This 
difference, if it exists, can be eliminated by slightly 
tilting the boards by means of wedges until each car 
when started will move down its incline with uniform 
speed. 

Inferences. — (a) Do your observations and results 
confirm the deductions of the theoretical discussion 
above ? 

(S) Make a general statement of what has been 
deduced and verified. 

(c) Explain briefly how you would use this method 
to measure out a pound mass of sugar or coffee at a 
place where you could not make use of the weight 
method. 



18 LABORATORY EXERCISES IN PHYSICS 
Exercise Number 6 

density of a regular solid 
References 



A 155 


GE6, 114 


H &W59 


C49 


GP 147, 148 


L32 


C & C 140, 141 


H 145 

W & H 15 


M & T 28, 31, 32 



The Purpose is to find out how many grams of 
matter there are in a cubic centimeter of a given reg- 
ular solid, i.e. to determine the density of the sub- 
stance of which it is composed. 

Operations. — (a) Determine the volume of the 
solid by the method or methods designated by the 
instructor, and in accordance with the directions 
given in Appendix C. 

(i) Determine the mass of the solid with the equal 
arm balance, trip scales or Jolly balance, according 
to the choice of the teacher. Follow the directions 
for the method chosen, which will be found in Ap- 
pendix D. 

Data and Calculations. — Since the density is the 
number of grams in one cubic centimeter, it is 
expressed by the quotient obtained by dividing the 
number of grams by the number of cubic centime- 
ters, and is denoted by the symbol ^ 3 , read grams- 
per-cubic-centimeter. Label all parts of the calcu- 
lation, so that it will explain itself. All the indi- 
vidual measurements of the dimensions and the 
weights should be tabulated in neat parallel columns 
similar to those used in the preceding exercises. If 



MECHANICS OF SOLIDS 19 

the volume or the mass has been determined by more 
than one method, the mean, or average volume or 
mass should be used in calculating the density. 

Record the name, form, arid substance of the 
solid used. 

Lessons. — (a) State any ways in which you think 
a knowledge of the density of a substance may be 
useful. 

(b) Supposing you know the density of a chip 
from a large, regular block of stone, explain how 
with the aid of this knowledge and a metric rule 
you could find the mass of the stone. 



Exercise Number 7 

ELASTIC FORCE OF A HELICAL SPRING 

References 

Clll GP40 W&H 23-25 

If & T 305 

The Purpose of this experiment is to find out 
what effect equal additions of force will have upon 
the length of a helical spring, and to learn how such 
a spring may be used as a dynamometer {i.e. a 
measurer of forces). 

Apparatus. — (a) The spring Fig. ± is suspended 
from a convenient support, and has a marker near 
its lower end, which moves over a convenient scale 
<jual parts, such as a metric rule. The common 
spring balance is such a spring, and has a scale of 
equal parts. The units of this scale may he marked 
pounds, ounces, or grams; and these units may be 



20 



LABORATORY EXERCISES IN PHYSICS 



again divided into fractional parts, (i) There may 
be either a hook or a pan for suspending masses so 
that the weights of these masses 
will pull on the spring, and 
SIWQ extend it more or less accord - 
I §-w") i n g to the magnitude of the 
pull, (c) A set of masses, such 
as the so-called weights used 
with a common balance is pro- 
vided, for exerting these pulls. 
Operations. — (a) A reading is 
first taken with no load on the 
spring. If a spring balance is 
used, and it is correct, the scale 
reading corresponding to no 
pull will be zero. In reading 
=^w^ the positions of the points on 
the scale, great care should be 
taken to have the eye on the 
level with the point on the 
scale at which the reading is taken: otherwise the 
reading will appear to be greater or less than it 
really is. This kind of error is called parallax and 
it may be almost entirely avoided by placing a small 
mirror behind the marker, and keeping the eye in 
such a position that the marker hides its reflected 
image, (b) A mass sufficient to elongate the spring 
by a readable amount is now placed on the pan (or 
hook), and the amount of the pull exerted by the 
weight of this mass is recorded (in grams-weight, 
or in dynes as the teacher may direct. Remember, 




Fig. 4. 



MECHANICS OF SOLIDS 21 

1 gm.-wt. = 980 dynes). The new scale reading is 
recorded opposite the pull that produced it. (c) 
The process of increasing the pulls, and of observ- 
ing the corresponding readings is continued until 
ten or more sets of readings have been taken, the 
pulls and scale readings being tabulated in parallel 
columns, (d) After each reading, the observer 
removes all weight, and notes whether the pointer 
returns to its initial reading. If it does not so 
return, the load has permanently stretched the spring, 
and further observations are of no value. 

Numerical Data. — If a spring balance graduated 
in grams was used, and if the weights were ex- 
pressed in grams, the table of data gives the correct 
value in grams-force of each scale reading re- 
corded. If a scale reading is greater than the 
weight that produced it by a certain amount, it is 
said to have a positive ( + ) error of that amount; 
and if any reading is less than the weight that pro- 
duced it by a certain amount, it is said to have a 
negative (— ) error of that amount. Look carefully at 
the numbers in the two columns, and see if the scale 
readings always increase by equal amounts when 
the stretching force (i.e. the weight) is increased by 
equal amounts. 

Inferences. — Answer in complete sentences — (ft) 
If f and/!, represent any two stretching forces, and 
e x and e 2 the corresponding elongations of the 
spring, do you find (neglecting small experimental 

errors) that *) = tl ? 



22 LABORATORY EXERCISES IN PHYSICS 

(b) State the numerical relation which you have 
found to exist (as far as your experiments go) be- 
tween the elongations of the helical spring and the 
corresponding stretching forces. This relation is 
known as Hooke's Law, because it was first stated 
by Eobert Hooke in 1678. 

(c) Do you think that a spring balance may be 
used conveniently for measuring forces ? Give 
your reasons. What advantage has a dynamometer 
over a set of masses for this purpose ? 

Sources of Error.— Briefly enumerate the sources 
from which you think errors may arise, and suggest 
any ways of avoiding them. 

Exercise Number 8 

GRAPHICAL REPRESENTATION. RELATION OF STRETCH- 
ING FORCE TO ELONGATION 

References 

Exercise Number 3. M & T 4, 5 

The Purpose is to plot a graph that will show the 
relation between the stretching force, exerted on the 
helical spring of the preceding Exercise, and the re- 
sulting elongation of the spring. 

Operations. — Let the abscissas represent the 
stretching forces, and the ordinates the corresponding 
elongations. The scales on which these quantities 
are represented should be chosen so that the graph 
fits the size of the page; the data for the graph should 
be tabulated near it; and the plotting should be 
done just as in Exercise 3. The parts of the dia- 



MECHANICS OF SOLIDS 23 

gram are to be fully lettered and labeled, as before, 
so that it will tell its own story. 

Inferences. — (a) If you had not already learned 
the relation between stretching forces and elonga- 
tions from the tabulated numerical data, would this 
graph tell you what it is ? (5) State the relation. 
How does the graph show it ? (c) If this graph has 
been made from data obtained w T ith a spring balance, 
explain how it may be used to find the correct value 
of the pull that corresponds to any given reading on 
the scale of the balance. A graph used in this way 
is called a calibration graph, and the process of 
testing the readings by comparison with known val- 
ues is called calibration. 

Note. — The elastic force with which the spring 
resists elongation is always equal to the stretching 
force, and Hooke's law is often stated in this way, 
"The force of restitution is proportional to the dis- 
placement '." The motion of such an elastic body 
when it is set in vibration is called Simple Harmonic 
Motion. 

Exercise Number 9 

PULLEYS 

References 

A 137-139 GE77-7!) H & W 101 

C 75-77 GP 80-82 L 137-138 

C & C 92, 9S-100 II 93, 107-1 10 W & H 39, 212 

M & T 33-37, 43, 70, 77, p. 95 

The Purpose of the exercise is to experiment with 
different arrangements of pulleys in order to find 



24 LABORATORY EXERCISES IN PHYSICS 

out how great a resistance can be overcome by a 
given force, and to determine the efficiency of a 
given arrangement for different loads. 

The Apparatus consists of a pair of pulleys, flex- 
ible cord, a pan of known weight, and a metric rule. 

Preliminary Study.— (a) With any arrangement of 
pulleys (Fig. 5), if there were no friction, how 
would the pull at any cross section of the cord com- 
pare with that at any other cross section ? 

(5) When a single, fixed pulley is used (A, Fig. 
5), how should the magnitudes of two forces f 2 and 
/ compare with each other when there is equilib- 
rium or uniform motion without friction ? 




Fig. 5. 



MECHANICS OF SOLIDS 25 

(c) With a single fixed pulley, is any advantage 
gained in applying a force, except that of changing 
the direction of the pull ? 

(d) With a single movable pulley (i?, Fig. 5) 
what two parts of the cord support the movable 
pulley and its load ? How do the upward pulls of 
these two parts of the cord compare with each 
other ? How does their sum compare with the sum 
of the weights of the pulley and its load ? Then, if 
the weight of the pulley, and the frictional resist- 
ance were negligible, how should the resistance f 
compare with the effort f x when the number of 
parts of the cord supporting the movable pulley 
is 2? 

(e) All other things remaining the same will the 
ratio of resistance to effort be changed if the free 
end of the cord from movable pulley C is passed 
over a fixed pulley Z>, so as to pull downward at D 
instead of upward at B ? 

(/*) In the fourth arrangement, the pulleys Cand 
D are changed to the positions C and D', the 
arrangement having been turned end for end. How 
many equal forces now support the movable pulley 
D' ? What is now the ratio of total resistance to 
f v the effort applied ? This ratio is called the 
mechanical advantage of the device. How does the 
mechanical advantage in each of the last three 
arrangements compare with the number of parts of 
the cord that support the movable pulley ? 

(g) Test your answers by hanging on a weight for 
f 2 in each case, and finding what I>ull/' l will balance 



26 LABORATORY EXERCISES IN PHYSICS 

it, or allow it to ascend or descend with uniform 

speed. Is the ratio -> 2 in each case nearly equal to 

J 1 
the number of parts of the cord that support the 

movable pulley? 

Operations. — (a) With the pulleys arranged as at 
CD or C f _/?', Fig. 5, attach to the movable pulley a 
mass whose weight f 2 is greater than that of the 
pulley, and find by trial the number of grams-weight 
at f x (including that of the pan) that will just lift 
the load f 2 with uniform speed. Measure the dis- 
tance l ± through which f x moves while f 2 moves a 
distance l 2 (of, say, 10 cm.). Calculate f 1 X l v the 
work in gram-centimeters done by the effort/^, and 
also f 2 X Z 2 , the corresponding work done on the 
resistance f 2 . Calculate also the efficiency, i.e. 
Useful work done f 2 X l 2 

Total energy expended f x X l x 

(b) Now diminish the weight f so it will just 
allow f 2 to descend with uniform speed, and calcu- 
late the amounts of work and the efficiency as before. 
The average of these two determinations of the 
efficiency is the mean efficiency for the given load. 

(c) In the same way, find the mean efficiencies 
for as many other loads as the time will permit 
using a considerably heavier load each time. 

Data. — Tabulate all symbols and data. 

(b) Plot a graph showing the relation between 
loads (taken as abscissas) and the mean efficiencies 
corresponding (taken as ordinates). 

Inferences.— Answer in complete sentences. 



MECHANICS OF SOLIDS 27 

(a) Do the data show that the efficiency of a given 
arrangement of pulleys increases with the load I 

(b) Does the graph show that the efficiency in- 
creases in direct proportion to the load, or in greater 
proportion, or in less proportion ? How ? 

(<?) From the number of gram-centimeters of work, 
how may you calculate the number of ergs ? The 
number of Kilogram-meters ? 

(d) In what ways have you seen pulleys used { 
Errors.— What do you consider the chief sources 
of error in this experiment ? What error is elimi- 
nated by having /a first ascend and then descend ? 

Exercise Number 10 

CONCURRENT FORCES 
References 

A 67-72 GE 41-44, 54-56 H & W 82-83 

C 57, 63 GP 42-45, 56-58 L 25, 96-106 

C & C 45-47 H 47-49 M & T 44-60 

Purpose. — The purpose of this experiment is to 
verify the principle of parallelogram of forces ; that 
is, to compound sets of forces in accordance with this 
principle, and find whether the force thus determined 
is the true resultant. 

Apparatus. — The arrangement is shown in the 
diagram. Three spring balances are used, to meas- 
ure the forces exerted by the cords and lengths of 
plumber's safety chain. The chains are joined to 
cadi other and to the balances by small key rings or 
harness rings so that they lie perfectly llat ; and the 




Fig. 6. — Apparatus arranged for experimenting with concurrent forces 



MECHANICS OF SOLIDS 29 

cords are secured at any desired points at the edges 
of the table by clamp hooks provided with thumb 
nuts. 

Operations. — (a) Let each of three students pull 
steadily on a balance and secure it to a clamp hook. 
Let the pulls be made at random, in any convenient 
directions and with any convenient forces, but so that 
equilibrium shall result. 

(5) A note-book page is to be slipped under the 
chains by a fourth student, who, when the equilib- 
rium is secured, marks on the page the positions of 
the chains. This he does by thrusting a pin through 
the links, exactly in the middle line of the chain, and 
pricking two points 1 1, 2 2, 3 3, for each line. The 
points should be as far apart as possible. Each line 
is to be marked with a letter, which will represent the 
force in the tabular form. 

(<?) At the same time the other three students 
record the readings of their respective balances. 

(cZ) The positions of the corresponding lines of 
direction being fixed, and the lines drawn meeting at 
a point, record the magnitudes of the forces on their 
respective lines, remembering to add the proper zero 
correction for each balance, ( 

(e) Let each student in turn get at least one such 
set of lines in his note-book; and using these lines. 
construct the parallelogram of the forces so recorded. 

Employing any convenient scale, cut off each line 
proportional in length to the magnitude of the Force 
it is to represent. 

Taking any two of these lines as adjacent sides, 



30 LABORATORY EXERCISES IN PHYSICS 

complete a parallelogram, and draw the diagonal 
from the meeting point of the three lines (point of 
application) to the opposite vertex. The chosen 
scale must be small enough so that the whole diagram 
will go on the page. 

(/) To find the numerical value of the resultant, 
measure this diagonal and multiply its length by 
the number of units of force that one centimeter of its 
length represents. Kecord the resulting value on 
the diagram. 

Zero Correction. — When used horizontally, a spring 
balance graduated to be used in a vertical position 
gives a small negative reading under no load. 
(Why ?) This is called the zero error and its 
amount must be obtained as follows : Hold the 
balance in the vertical position, and slowly change 
it to the horizontal, lightly tapping it the while. 
(Why?) 

Take off on a pair of dividers, or a straight-edged 
bit of paper, the length of the zero error ; and apply 
it to the scale of the balance so as to measure its 
amount in scale units and tenths. Since all horizontal 
readings of the balance will be smaller than they 
ought to be by just this amount, each reading must 
be corrected by adding to it the amount of the zero 
error. The readings thus corrected give the real 
values of the forces observed. 

Data. — Record (a) the scale of the diagram ; 
(5) the values of all four forces (corrected balance 
readings in pounds and tenths, or in grams); 
(e) lengths of all four lines which represent the 



MECHANICS OF SOLIDS 



31 



forces ; (c?) name the lines representing both compo- 
nents, the resultant and the equilibrant, and show 
their directions by arrow tips ; (V) record the amount 
and per cent of the experimental error, i.e. the differ- 
ence between the numerical values of the equilibrant 
and of the resultant. 

Place the data near the diagram in tabular form, 
as below. 



Scale of the Diagram . . . . 
Numerical Data 



Name of Force 


Force 
(Letters) 


Balance 
Reading 


Zero 
Correction 


Force 

Amount 

IN LBS. or gm. 


Length 

of Line 


Component 












Component 












Equilibrant 












Resultant 












Experimental 
error 




Per cent error 





Sources of Error. — Errors may arise from (a) 
parallax; (6) friction of the balances, chains, or 
cords; (//) inaccuracies in construction and meas- 
urement. Friction may be avoided by lightly tap- 



32 LABORATORY EXERCISES IN PHYSICS 

ping the balances and cords to allow them to come 
into position in straight lines. 

In constructing the parallelogram, see that the 
pencil is kept sharp and the dividers in good condi- 
tion. Use the utmost care. If all the work is care- 
fully done, the per cent of error will be small. To 
compute the per cent of error, multiply the error by 
100 and divide by the value of the equilibrant, which 
may be taken as the base. A given error will be less 
important in proportion as the base is large. Hence 
use forces as large as practicable. 

Inferences. — Answer, in concise sentences, the fol- 
lowing questions : (a) Neglecting the experimental 
error, how does the resultant, as found in the experi- 
ment, compare in magnitude with the equilibrant ? 

(6) What is the direction of the resultant with 
reference to that of the equilibrant? 

(<?) Do you, therefore, conclude that the quantity 
determined in your experiment, and recorded as the 
resultant of the two forces^ that were chosen as com- 
ponents, is the true value of their resultant ? Copy 
and memorize the Principle of the Parallelogram of 
Forces as stated below. 

Principle Verified. — If two forces, acting at an 
angle upon the same point, be represented in direc- 
tion and magnitude by two lines drawn to any given 
scale, then the resultant of these two forces will be 
completely represented, on the same scale, by the 
concurrent diagonal of the parallelogram constructed 
upon those two lines as adjacent sides. 

Addition of Vectors. — Any line representing a 



MECHANICS OF SOLIDS 33 

force, motion, or other quantity having both direc- 
tion and magnitude is called a vector. The length 
of the vector shows the magnitude of the quantity, 
and the direction of the vector, as given by the 
arrow tip, shows the direction of the quantity. 
Since the diagonal of a parallelogram divides it into 
two equal triangles, and is the third side of either 
triangle, it may be found without constructing the 
whole parallelogram, as follows: Draw a vector 
representing either component in direction and 
magnitude, and from the end of the first vector, 
draw the vector representing the second component 
in both direction and magnitude. Then the line 
drawn from the leg inning of the first vector to the 
end of the last is the vector that represents the 
resultant in direction and magnitude on the same 
scale as that by which the components are repre- 
sented. This process is called the addition of vec- 
tors. The resultant of any number of forces that 
act on a single point, may he found hy adding tJu ir 
vectors, end to end, in any order. The resultant vec- 
tor is that drawn from the beginning of the first to 
the end of the last; and the equilibrant vector is that 
drawn from the end of the last to the beginning of 
the first. If the vectors of any number of forces act- 
ing on a single point form a dosed figure when added 
In any order, It may be known that this system of 
forces will be In equilibrium. This method is much 
used by engineers, in finding the proper strengths 
of tie rods and struts or posts in framed structure-, 
such as bridges, roofs and steel frames of buildings. 



34 LABORATORY EXERCISES IN PHYSICS 

The student should get into the habit of looking for 
such sets of forces. They are found in the cases of 
sailboats, kites, bicycle frames, jib cranes, machinery, 
the poles where electric lights and trolley wires are 
suspended, and all kinds of structural work, such as 
roof trusses and bridge frames. 

i Exercise Number 11 

\ 

WORK. INCLINED PLANE 

References 

A 80, 121-127, 140, 141 H 53, 60-62, 94, 111 

C 64-66, 69, 71-73, 78 H & W 87, 97, 102 

C & C 48, 89-92, 101-103 L 77-80, 93, 137 

GE 67, 71-73, 77, 78, 83 M & T 53-61 

GP 62, 70, 74-76, 80, 86 W & H 46, 199-203, 206 

The Purpose of the experiment is to find out what 
force, applied parallel to an inclined plane, will lift 
a given weight, and to learn how the work done by 
this force compares in amount with that of lifting 
the weight vertically through the same height. 

Apparatus. — A car, and some iron nuts or other 
weights, and an inclined plane, are placed as shown. 
A spring balance is attached to the car by a short 
stout cord. A metric rule and a pail or basket, 
or the trip scales and weights are also provided. 

Operations and Data. — Holding the balance parallel 
to the plane, and keeping the line of sight perpen- 
dicular to the plane of the scale at the point of 



MECHANICS OF SOLIDS 



35 




reading, move the car up and down the plane, and 

read the amount of 
the force indicated 
while a uniform velo- 
city is maintained. 
With the usual pre- 
cautions, take the 
measurements of the 
quantities indicated 

Fig. 7. — Showing how the force is below : 

applied and observed. 7 . 

A, the height of 
the plane from floor to the point vertically above 
the table edge. 

Z, the length of the plane from floor to the same 
point. 

2, the zero correction for the balance in position. 

u, force required to maintain uniform velocity up 
the plane. 

d, force required to maintain uniform velocity 
doivn the plane. 



/. - 



u + 



t — V the mean force required to balance 

the component of weight of car and load along the plane. 

F, ( = / — z), the mean force as above, corrected 
for zero error. 

IF, the combined weight of the car and its load. 
This weight may be obtained directly with the trip 
scales, or by suspending the car and load in a pail 
or basket on the hook of a spring balance, the weight 
of the pail or basket being subtracted from the total 
weight in order to get the value of W. 



36 



LABORATORY EXERCISES IN PHYSICS 



Data 
Observations made by... 



Fx I, the work done along the displacement I, by 
the force F. 

W X A, the work done in moving the mass against 
the resistance Wj through the vertical displace- 
ment h 

e, the experimental error. 

The values of h and I are to be taken in inches to 
the nearest Jth, and reduced to feet and hundredths; 
balance readings in pounds and tenths. Or if forces 
are recorded in grams, the distances must be in centi- 
meters; and if forces are recorded in kilograms, the 
distances must be in meters. The amounts of work 
will then be 
in foot-pounds, 
or gram - centi- 
meters, or kilo- 
gram-meters re- 
spectively. If 
so directed by 
the teacher re- 
duce the work in 
gm.-cm. to ergs. 
To do this mul- 
tiply by 980. 
Why? Tabulate 
as here: — 

Calculations. — The amount of error is the numerical 
difference between Fxl and ir X h. The percent- 
age error is calculated by finding what per cent this 
difference is of the mean value of the two amounts 
of work. 




MECHANICS OF SOLIDS 37 

Sources of Error. — State the sources of the errors 
pertaining to (a) the length measurements, (J) the 
balance readings, (?) the positions of the balances 
and cord in moving along the incline. 

Inferences. — (#) Judging by your observations 
and the experience of the others in the class, do you 
think it fair to infer that the difference between the 
corresponding values of W x h and F x I are wholly 
due to experimental errors ? (Why ?) 

(6) Make a complete and general but concise state- 
ment of the relation existing between the quantities 
of work compared. 

ADDITIONAL PROBLEMS 
(Voluntary, or assigned at the option of the teacher.) 

(a) If you are satisfied from your experiments that the equa- 
tion Wh = Fl is correct (neglecting friction), find the value of 

W 
the mechanical advantage r= of any inclined plane in terms 

of its dimensions / and h. 

(b) Make the slope of the plane steeper or less steep, measure 
I and h, and also measure either W or F. You now have three 
out of the four quantities of the equation: calculate the fourth 
quantity. Now measure this quantity as in the experiment, 
and see how near its value is to that predicted by the calcula- 
tion from the equation. What is your opinion as to the utility 
of the equation? If the slope is made less steep, can a greater 
weight W be lifted by a given effort F ? In this case, can more 
work be done by it when exerted through the same distance? 

(c) Draw a diagram of the plane, using a convenient scale 
for the length I and height h. Using another convenient scale 
for the forces, represenl the weight W by a vector drawn from 
a point on the plane (in what direction?). Draw a vector to 
represenl the direction of the component of the car's weight 
that is tending to make it travel downward along the plane. 



38 LABORATORY EXERCISES IN PHYSICS 

(What should be the direction of this vector?) Does the car 
also push perpendicularly against the plane? How could you 
prove this? Represent the direction of this push also by a 
vector. (What direction?) Is this push also a component of 
the weight IE? Why? Since you are not supposed to have 
measured the two component forces, you drew the vectors of 
indefinite length; and you have a side and two adjacent angles 
of a triangle: complete this triangle. The lengths of the two 
component vectors are now determined: measure each and 
multiply it by the scale number: what do the resulting num- 
bers represent? Compare the value of the component F, par- 
allel to the plane, as obtained from the vector diagram, w r ith its 
value as measured by a spring balance or a weight hung from 
a cord and passed over a pulley. Compare the value of the 
push of the car against the plane as obtained by the vector 
method with the value of it as obtained by measuring the pull 
of the car against a spring balance applied so that it w T ill just 
lift the car off the plane in a direction perpendicular to the 
plane. 

(d) For a case of the car on the plane, measure (1) the force f lf 
parallel to the plane, that will hold the car in equilibrium; (2), 
the weight f 2 of the car; (3), the resistance / 3 of the plane to the 
perpendicular push of the car. Xow represent these forces by 
vectors drawn end to end in any order, each of the proper direc- 
tion and magnitude for the force it is to stand for. Does the 
end of the last line meet the beginning of the first, so as to 
form a closed triangle? (Cf. Addition of Vectors, Exercise 10, 
p. 33.) 

(e) Draw the vector diagram of the plane and forces for any 

case of the inclined plane where the force F is applied parallel 

the length I, and lifts a weight TT T through the corresponding 

vertical distance h; and prove by the geometry of similar tri- 

W I 
angles that — = — hence Wh = Fl. 

(/) Determine the efficiency of the inclined plane with a 
given slope, and for one or more loads just as was done for the 
pulleys in Exercise 9. What kinds of useless work are done in 
the case of the inclined plane? 



MECHANICS OF SOLIDS 



39 



Exercise Number 12 

strut and tie. resolution of forces 
References 
A 58 GE 56 H & W 82, 83 

C-21,57 GP62 L 102 

C & C 38, 48 H 53 M & T 44-58 

W & H 46 

Definitions. — Fig. 8 represents an arrangement of 
beams or posts, or rods, p c a, b a, and b c y exert- 
ing balanced forces at points J, e, and a. These 
beams, posts, or rods are found in all structural 

x 




Fig. 8. 

work, cranes, etc., and are called members. If a 
member has to exert a push or thrust, it is called a 
strut; and if it is under tension and has to exert a 
pull, it is called a tie. In a crane b c is called the 
boom, and post p c a is called the mast. 

The Purpose of the experiment is to find out 
whether the weight W of the suspended mass may 
be conceived to be resolved at 1> into two component 
forces, one of which, A', exerts a push against the 
strut in the direction h r, and the other, Y, 8 pull on 
the tie in the direction a b. 



4:0 LABORATORY EXERCISES IN PHYSICS 

The Apparatus consists of the post, strut, tie-cord, 
suspended mass and spring balances, M and JV, 
Fig. 8. The spring balances may be supported in 
their positions (by resting them on pegs or wire 
nails driven into a large vertical board behind the 
apparatus) in order that their weights may not act 
as forces and introduce errors into the measure- 
ments. The strut is not fastened to the post, but is 
held by the pressure of the cord, and its weight is 
supported by a wire nail or peg near its middle 
point. 

Operations. — (a) Weigh the mass. 

(h) Measure each of the angles #, <?, and J, with a 
protractor, or by placing a card behind each angle 
and pricking a hole with a pin at the vertex of the 
angle and at a point of each of its sides. 

(c) On your note book page, represent W by a 
vector j? q, drawn to a suitable scale; and complete 
the vector triangle for the three forces W, X, and 
Y. To do this, draw from p a line of indefinite 
length and having the direction of one of the com- 
ponents Y or X, and then from q another line of 
indefinite length, having the direction of the other 
component X or JT, and intersecting the vector of 
the first component in a point r or s. The directions 
may be determined by the angles. Thus the angle 
qps or pqr = the angle c\ and the angle p q s or 
q p r — the angle a. Then p s or r q is the vectoi' 
that represents X in direction and magnitude, and 
s q or p r is the vector that represents Y. Measure 
the vectors for X and Y and multiply by the scale 



MECHANICS OF SOLIDS 41 

number, to get the magnitudes of these compo- 
nents. 

(d) Pull cautiously on the spring balance M in 
the direction c h until the strut c h just falls. The 
pull will then be just equal to X r the thrust of the 
strut, and also just equal and opposite to the com- 
ponent X, which X f was holding in equilibrium. 
(The .reading of the balance should be corrected for 
zero error, cf. Exercise 10 p. 30.) This corrected 
balance reading is the magnitude of X ; , and also of 
the required component X. 

(e) Read the spring balance N. Its reading (cor- 
rected for zero error, cf. Exercise 11 p. 35) is the 
value of the component I^and also of the equal and 
opposite pull Y r of the tie b a. 

Numerical Data. — (a) Record on the vector dia- 
gram the lengths of the three vectors, and the 
magnitude of the force represented by each. 

(b) In a suitable ruled form, tabulate the values 
of TF, X, and ^obtained from the vector diagram, 
and also those obtained by direct measurement, so 
that they may be compared. Record also the zero 
corrections, and the amounts by which the cor- 
rected balance readings for X and Y differ from 
their respective values obtained by the vector 
method. These differences are the experimental 
errors, and will be smaller and smaller as more care 
is taken in the experiment. 

(c) Indicate the directions of the weight IT and 
the components X and Y by arrow points on the 
diagram. 



42 LABORATORY EXERCISES IN PHYSICS 

Inferences. — Answer in complete sentences: (a) 
Are the values of the components X and Y pre- 
dicted by the vector method very nearly equal to 
their measured values ? 

(b) What is your opinion as to the existence of 
the predicted components X and J 7 , and as to the 
practical value of the vector method for determining 
the magnitudes of such forces when they cannot be 
conveniently measured ? 

Sources of Error. — Briefly state what you consider 
to be the most important errors in the experiment. 

OPTIONAL PROBLEM 
Add in any order the vectors that represent the three 
balanced forces, W, X' , and Y' ' ; and see if these vectors form 
a closed triangle. What is your opinion as to the value of 
this construction in testing the calculations in structural 
problems similar to that in this experiment? 

Exercise Number 13 
levers. moments 

References 

A 128-133 GE 47-49, 81 H & W 84, 99 

C 60-62, 74 GP 49-51, 84 L 113, 137 

C & C 93-95 H 96-103 M & T 62-69 

W & H 49-54 

The Purpose is to find out how great an effort 
must be applied to overcome a given resistance with 
a given lever, or how great a resistance may be 
overcome with a given effort, also the conditions 
under which a lever will be in equilibrium. 

Apparatus.— A convenient lever for this purpose 
is a meter stick, or half of one, used as m Fig. 9. 



MECHANICS OF SOLIDS 



±3 



/>p 



The effort and resistance may be represented by 
the weights of certain masses freely suspended 
from any chosen points along the bar. If a pan is 
used to hold the mass- q 

es at either point, 
the weight of the pan 
must be added to that 
of the mass which it 
supports, to get the 
total force applied at 
that point. The prob- 
lem is much simpli- 
fied by keeping the 
fulcrum [i.e. the axis 
at which the lever is 
supported, and about 
which it turns) at the 
middle point of the 
bar. By this arrangement the weight of the bar can 
have no moment (i.e. no turning effect) about the 
fulcrum; and so it may be neglected without intro- 
ducing any error. 

Operations.— (a) Suspend a known weight f 2 at p 2 
having any convenient distance from the fulcrum jp a ; 
and at some other point p x having a distance from 
p greater than that of yv suspend just enough 
weight to keej) the lever in equilibrium in a hori- 
zontal position. | It is not necessary to wait for the 
lever to come to rest ; for if it swings through equal 
distances on opposite sides of the horizontal position 
it will be horizontal when it does come to rest.) 





Fig. 9. 



44: LABORATORY EXERCISES IN PHYSICS 

(i) Apply some different known weight for the 
effort f x at the same point jp^ and see what new 
resistance /!, it will balance at^? 2 . 

(c) Repeat the experiments, changing the arms 
of the forces (i.e. _p B p 1 and p 3 j? 2 ^ the perpendicular 
distances from the axis to the lines of direction of 

the forces) so that the ratio - — ; will be 

Resistance arm 

changed. 

Data and Calculations.— For each experiment, cal- 
culate the moments of the effort and the resistance 
respectively (i.e. moment equals force X arm of 
force). Tabulate the following data in parallel col- 
umns one for each experiment, — Effort, Effort 
arm, Moment of effort, Resistance, Resistance arm, 
Moment of resistance, Experimental error. Place 
under the head of experimental error any differences 
between the numerical values of moment of effort 
and corresponding moment of resistance. 

Inferences.— Answer in complete sentences, (a) 
Do the differences between the moments of effort and 
the corresponding moments of resistance approach 
to zero as more care is taken ? Are you therefore 
correct in assuming these differences to be experi- 
mental errors ? 

(b) If these differences may be made so small as 
to be negligible, what equation may be inferred for 
the lever when balanced ? 

OPTIONAL PROBLEMS 
(a) Repeat the experiments with the bar supported at 
p 3 by a spring balance or by a pan of weights attached to a 



MECHANICS OF SOLIDS 45 

cord that passes over a pulley, and see if in each case the up- 
ward force exerted by the fulcrum at p 3 equals the sum of 
the two downward forces p x and p 2 plus the weight of the bar. 
(b) If } x and / 2 are two opposing forces acting about an 
axis, and if a x and a 2 are the corresponding arms, and if it was 
proved by your experiments that f x X cl\ = h X a 2 , show that 

t=— • For each case, take from your table of data the 

/l «2 

values of these four quantities, compute the two ratios, express- 
ing them decimally, and see how nearly equal they are. The 

Resistance 

ratio, — t^ is called the mechanical advantaqe of the 

Effort 

contrivance. May we say that the mechanical advantage of a 

lever is equal to the ratio of the effort arm to the resistance 

arm? If you know the mechanical advantage and either of 

the two forces, effort or resistance, show how the other may 

be found by a simple calculation. 

(c) Experiment by hanging a weight that represents the 
resistance / 2 at the middle point (now called p 2 ) of the bar, 
and suspending the bar in a horizontal position at any two 
points p l and p 3 on opposite sides of p 2 . Let p 3 now be the 
fulcrum or axis about which the effort f 1 of the first spring 
balance is to turn the bar in order to lift the weight / 2 . The 
arm of the effort / 2 with respect to the new axis p 3 is now p 3 p 1 ; 
and the arm of the resistance is p 3 p 2 . Measure the forces 
and their arms; calculate their moments with respect to p 3 ; 
and see if these moments are equal. Remember to allow 
for the weight of the bar by finding its effect on the balance 
at p x when there is no load at p 2 and subtracting this amount 
from the balance reading at pj. Try different forces and arms 
and tabulate the quantities as before. Calculate the mechan- 
ical advantage for any given case; and with it compute the 
effort required to lift a known resistance, or the resistance 
that a known effort will overcome; and then test by experi- 
ment to see how nearly the calculated value agrees with that 
obtained by trial. 

(d) For a given case, determine the work done by the 

effort and that done by t lie resistance, alsothe mean efficiencies, 

after the manner of the experiment with the pulley- />. Re- 
peat with the fulcrum somewhere else than at the middle of 



46 LABORATORY EXERCISES IN PHYSICS 

the bar, and compare results. Is the efficiency greater when 
the middle part of the bar is on the effort side of the fulcrum 
or when it is on the resistance side? Can you explain why? 
(e) Call the measured vertical distances through which 
/ 2 and /j move (as determined in the preceding problem) 
l 2 and l x respectively. See if the mechanical advantage equals 

j- == — = Y- Can you prove by the geometry of similar 
/i a 2 h 

triangles that the last two ratios should be equal if the effect 
j of the weight of the bar were eliminated? Prove that f 2 l 2 = 
/ x li , i. e. the work done on the resistance equals that done by 
the effort. 



Exercise Number 14 

wheel and axle. moments 

Note. — At the option of the teacher, a part of the class may 
work on this experiment while the other part works on Exercise 
13. 

References 
A 134-136 GP 85 L 137 

C & C 96, 97 H 104, 106 M & T 66, 75 

GE82 W&W100 W&H211 

The Purpose is similar to that of Exercise 13. 
State it. 

Apparatus.— The wheel-and-axle, Fig. 10, consists 
of two cylinders turning about an axis to which both 
are fixed. The forces are applied by cords wound 
round the circumferences of the wheel and the axle 
in opposite directions, so that one is wound up when 
ihe other is unwound. The winch, the capstan, and 
the pilot wheel of a boat (see dictionary) are modi- 
fications in which the effort is applied at the end of 
a bar or handle. 



MECH ASICS OF SOLIDS 



47 




h 



Operations. — The forces may be applied by attach- 
ing weights to the cords just as in the experiments 
with the lever or pulley, Exercises 
13 and 9. Xotice that the effort arm 
is the radius of the wheel and the 
resistance arm that of the axle, and 
that since the fulcrum is at their 
common axis, the weight of the 
wheel and axle has no turning effect. 

Find the efforts required to balance 
various resistances, and vice versa, 
just as directed for the lever in Ex- 2 
ercise 13, calculate the moments, 
tabulate all the data, and compare 
results as before. As there will be 
some friction, determine f 2 by add- 
ing weight at f x until f 2 rises with 
uniform velocity, and then removing 
weight at f x till f 2 descends with uniform velocity. 
The mean effort or f x is the average of these two 
weights, and the friction force is half their difference. 

Inferences.— (a) State whether or not the law of 
moments of the wheel and axle is identical with that 
of the lever. 

(h) State whether the ratio of the displacements 
of the effort and resistance {i.e. the vertical distan- 
ces through which they move) is equal to the ratio 
of their arms (i.e. the radii of the wheel and axle 
respectively). To find out, you may prove it by 
the geometry of the circle, or verify it by measure- 
ments in a number of cases. 




Fig. 10. 



48 LABORATORY EXERCISES IN PHYSICS 

OPTIONAL PROBLEMS 

(a) Efficiency. — Determine the efficiency of the wheel and 
axle for given loads just as directed for pulleys in Exercise 
9, and express the relation of efficiencies to loads by a graph. 

(6) Experiments with a Dissected Clock. — 1. With the 
aid of the printed directions in the box, assemble the clock. 
2. Is the wheel and axle part of the clock motor like that of a 
derrick except that the clock "weight" descends and drives 
the gear, instead of being lifted by it? 3. Determine the 
lbs.-wt. of the "weight," and the distance it falls in one hour. 
Calculate the horsepower of the clock. 

Exercise Number 15 

PARALLEL FORCES AND THE LAW OP MOMENTS 

References 

A 69, 128-132, 134, 135 H 96-105 

C 60, 63, 74-77 H & W 84, 85, 99 

C & C 47, 93-97 L 53, 107-109, 113-117, 127, 137 

GE 45-49, 81-83 M & T 62-70 

GP 19, 46-49, 84-85 W & H 49-54 

Purpose. — In this exercise it is proposed Qa) to 
investigate the laws of equilibrium for three parallel 
forces, and (J) to formulate a rule for determining 
the point of application, direction, and magnitude of 
the resultant of any given pair of parallel forces. 

Apparatus. — AB is half a meter stick, with wire 
nails passed through holes drilled at intervals along its 
axis, at right angles to its faces, and projecting about 
a half centimeter above and below ; c,c,c are pieces 
of stiff wire, bent into the form of clevises. Three 
spring balances, with cords and clamp hooks, are used 
to measure the forces, F v F 2 , F s , in a manner similar 



MECHANICS OF SOLIDS 



49 




F, CLEVIS 

Fig. 11 

forces are applied to the sus- 
pended bar, 



to that of Exercise 10. The bar is suspended by a 
wire, as shown, so that it hangs horizontally about a 

centimeter above the table. 
Operations. — (a) Arrange 
the balances so as to exert 
parallel forces as indicated 
in the diagram. At least 
four cases are to be made, 
by varying the relative dis- 
tances between the point of 
application, p 2 , of the mid- 
dle force and the points 
of application, p x and p v of 
3 the two end forces. These 
distances are varied by 
placing the clevises over 
different nails on the bar and moving the clamp 
hooks along the ends of the tables. 

The forces may be varied in amount by drawing 
the cords forward or backward at the clamps and 
securing them by the thumb nuts when the desired 
tension is attained. 

(b) Choose any convenient ratios for the distances 
p x p 2 and p 2 p v e.g. Case I, \ -; Case II, \ ; Case III, 
} or \ ; Case IV, \ or |. 

(?) Use the utmost care to avoid friction in the bal- 
ances or cords, to have the forces act all parallel and 
in the same plane, and to see that the bar is in a hori- 
zontal position just clear of the table. Be sure that 
the plane of the wire that supports the weight of the 
bar is exactly vertical. 



50 



LABORATORY EXERCISES IN PHYSICS 



Data. — (a) For each case make a diagram. Rep- 
resent distances and forces each on a scale appropriate 
to the size of the page, e.g. for distances, 1 cm. = 
5 cm. ; for forces, 1 cm. = 2 lbs., or 1 cm. = 100 g. 
Do not crowd more than two cases on a page. 

(J) Above each diagram state the scale to which 
it is drawn. 

(<?) Underneath each diagram state what point is 
adopted as the centre of moments ; choose a different 
point for each case, but be sure to use that point only 
throughout that case. 

(c?) On the line representing each force, record its 
value in pounds and tenths, or in grams (corrected 
for zero error) ; also indicate its direction by an arrow 
point. 

(#) Near the line representing each arm, record its 
length in centimeters. 

Numerical Data 



Force 
(Letter) 


Balance 
Reading 


Zero 
Correction 


Force 
(Amount) 


Arm 


Moment 


F, 












F-2 












Fs 












Sum 




Sum 





(f) For each case fill out a tabular form as above. 
Be careful to give the dimensions of forces and arms 



MECHAXICS OF SOLIDS 51 

(lbs., g., or cm.) and the + or — signs of the forces, 
of the moments, and of the sums. If a force in one 
direction is called positive, one in the opposite direc- 
tion is negative ; and if a moment acting clockwise 
is called positive, one acting counter-clockwise is 
negative. 

The sums are understood to be the algebraic sums. 

Calculations. — Moment = force x arm. If the arm 
of any force = (i.e. if the centre of moments is iden- 
tical with the point of application of the force), the 
moment becomes 0. It should, however, be set down 
in its proper place. In solving the equation, form 
the habit of considering the moment of each force in 
turn from the left to right, not omitting any. 

Sources of Error. — State briefly the sources of 
error pertaining to the different parts of the appara- 
tus, and the operations and measurements, also the 
precautions necessary in order to minimize them. 

Inferences. — Frame a concise statement in answer 
to each of the following questions : (#) In order that 
three parallel forces in the same plane may be in 
equilibrium, what must be the numerical value of the 
algebraic sum of the forces, and also of the algebraic 
sum of the moments about any chosen point ? 

(6) If your results show small + or — quantities 
for the sums of the forces or of the moments, do you 
think they may fairly be regarded as due to experi- 
mental errors ? Why ? 

(c) Which of the conditions mentioned in (a) must 
be satisfied in order to prevent translator}* motion? 
and which to prevent rotary motion? 



52 LABORATORY EXERCISES IN PHYSICS 

(d) In each case, which force is the equilibrant of 
the other two, and how must their resultant compare 
with it in point of application, direction, and magni- 
tude ? 

(e) What, then, is the direction, and what the 
magnitude of the resultant of any two parallel forces, 
compared with those of the forces ? 

(/) How does the point of application of the re- 
sultant divide the line joining those of the two 
forces ? 

Additional Work. — If there is time for extra work, the stu- 
dents may experiment with four or more forces in the same 
manner as above, or repeat the experiment with the bar not 
perpendicular to the lines of direction of the forces. In the 
latter case they should remember to measure the arm of each 
force on a line perpendicular to its line of direction. 



Exercise Number 16 

centre op mass 

References 



A 94-95 


GE 50-53 


L 119, 120 


C 92-97 


GP 52-54 


M & T 71-74 


C & C 52, 54-56 


H 74, 75 


W & H 57, 58 



Purpose. — The purpose of this exercise is to locate 
the centre of a mass of a pasteboard triangle, and to 
determine its relation to the medians. 

Apparatus. — The apparatus consists of the paste- 
board triangle, a pin, and a plumb-line, which may- 
be a heavy button suspended by a thread. 



3IECHAXICS OF SOLIDS 53 

Operations. — (a) Pass the pin through the triangle. 
as near as possible to one vertex, and work it around 
in the hole till the triangle can oscillate freely 
about it. 

(l>) Tie the plumb-line to the pin. and drive the 
latter into the wall. Adjust the thread till it is 
very near the triangle, but not touching it. 

(?) Tap the triangle lightly, so that it will oscil- 
late and then come to rest. 

(d) By means of two line pencil-marks locate on 
the triangle the position of the vertical line through 
the point of suspension, as indicated by the plumb- 
line. 

(e) Repeat the operations for the other two ver- 
tices of the triangle. 

(/) Draw the lines on the triangle. If the work 
has been accurately done, they will meet in a point. 

Q<j) Test the accuracy of your work by observing 
whether you can balance the triangle upon a pin- 
point at the intersection. 

(It) Measure and record the distances from the 
points in which the lines intersect the sides of the 
triangle to the adjacent vertices. 

Data. — (a) Choosing a convenient scale, draw a 
diagram of the triangle, together with the lines 
mentioned in Operations (d) to (/). 

) Record, either in tabular form or upon the 
diagram itself, the measurements of Operation (K). 

(e) Record the fl ale of the diagram. 

Sources of Error. - Make a concise statement, 
pointing out the sources of error. 



54 LABORATORY EXERCISES IN PHYSICS 

Inferences. — Answer in brief, complete sentences, 
the following questions : — 

(a) Does each of the lines drawn in Operation (/) 
contain the centre of mass ? Why ? 

(5) How is the point determined ? Why ? 

(c) Are the lines medians of the triangle ? Why ? 

(d) What is the relation of the centre of mass to 
the centre of figure of any regular polygon ? 

(e) Would this be true if the polygon were not 
of uniform density and thickness ? 

(/) Where is the centre of mass with reference 
to the thickness of the triangle ? 

Additional Work. — If there is time for additional work, 
a good illustration of the practical value of this principle is 
to cut out to scale a pasteboard model of half a stone bridge 
arch, and by determining the centre of gravity of the model, 
locate the centre of gravity of the semi-arch. 

Note. — This exercise may profitably be performed by the 
students at their homes. 



Exercise Number 17 

equilibrant of parallel, forces. effect of the 
weight of a bar 

References 

A 69 ; 128-132 GE 74, 78, 50, 52, 81 H & W 99 

C 60, 63, 74-77 93, 94 GP 49, 50-54 L 120, 127, 137 

C & C 55, 93, 94 H 51, 96-105 M & T 66-69, 71, 72 

W & H 51-54, 59a 

The Purpose of the experiment is to determine by 
the law of moments the direction, magnitude and 
point of application of the single force that will 



MECHANICS OF SOLIDS 



55 



hold a number of parallel forces in equilibrium, the 
weight of the bar being one of these forces. 

The Apparatus consists of a bar made of a meter 
stick with a bent strip of lead on the end. Forces 
may be applied to it by hanging on it known 
weights by loops of thread at given points. 

Operations.— (a) Weigh the bar. If the bar were 
aniform, at what point might its weight be assumed 
to act? It is not 
uniform: therefore V 7 

determine its center 
of mass G by bal- 
ancing it in a loop 
or clevis without 
adding any load. 
Measure and record 
the distances of G 
from the two ends. 

(Jj) Hang a weight Fig. 12. 

W at a, and balance the bar as in Fig. 12. What 
should be the magnitude of the equilibrant E of the 
two downward forces [i.e. of W applied at a and 
the weight W t of the bar applied at G) ? 

(c) Measure a h. Write down the equation for 
the equilibrium of the moments with respect to an 
axis at I: thus, 

- WX a I + E Xch - W x X G I = 0. 
In this equation, all the quantities are known except 
ch\ for A'was given in the answer to the question 
in (b) above, and all the others were measured 
except c I. Substitute the values of the known 




56 LABORATORY EXERCISES IN PHYSICS 

quantities, and solve for c b. Now measure c b 
with a rule, and E with a spring balance, and see 
how nearly correct your calculation was. 

(d) Make a similar case, but with one or more 
other weights W^ TP^, etc. hung at any other 
points on the bar; and, leaving E and c b unmeas- 
ured, put the sum of all the moments equal to zero 
as before. Calculate E and c b\ then measure 
them, and compare calculated with measured values. 

Inferences. — In calculating the magnitude and 
location of the equilibrant or single force which 
holds the others in equilibrium, you assumed that 
when a system of forces is in equilibrium the algebraic 
sum of all the opposing forces is equal to zero, and 
the algebraic sum of all the moments about any given 
point is equal to zero. Did the results predicted by 
the calculations fit the facts closely ? If so, what is 
your opinion as to the truth of the principles 
assumed, and of their value as a basis of other cal- 
culations ? 

(b) What is your opinion as to whether or not the 
weight of a beam or girder in a bridge or other 
piece of structural work should be considered as one 
of the forces acting about any given point in the 
structure ? 

OPTIONAL PROBLEMS 

(a) For either case above, take the axis at a or 
any other point except c or J, and see if your calcu- 
lations, with the moments taken with respect to this 
new axis, give nearly the same results as before. 

(b) Make a case with the weight W of the bar 



MECHANICS OF SOLIDS 57 

unknown and all the other quantities measured, cal- 
culate IF, then measure it and compare results. 

(c) Make a case with G unknown, measure all 
the other quantities, and calculate G 1> so as to find 
the location of G with reference to the ends of the 
bar. See if the unloaded bar balances at G. 

(d) Suspend the bar at G its center of mass, hang 
an unknown mass at 5, and move the loop by which 
a known weight W is suspended along the bar till it 
balances the weight IT of the unknown mass. By 
the equation of moments with respect to G as in 
Exercise 13 with the lever, the unknown weight is 

JJ— ]y x p j . Calculate it, and compare with the 

value of XI as obtained with an ordinary balance. 
This is the principle used in "steel-yards." 

Exercise Number 18 
laws of the pendulum 

References 

A 106, 112-120 GE 60-63 H & W 74-81 

C 68, 87-89 GP 65-69 L 73, 141, 143 

C & C 68-77 H 8:5-1)1 M & T 308, 309, 

W & II 189-193 302-307 

Part A 

EFFECT OF LENGTH AND AMPLITUDE 

Purpose. — The purpose of Part A is twofold: 
(a) to learn whether the period of a pendulum is 




58 LABORATORY EXERCISES IN PHYSICS 

affected by the amplitude of vibration, and (J) to 
determine whether the period of a given pendulum 
varies directly as the square root of its length. More 
briefly, the aim is to verify the laws of the pendulum 
regarding amplitude and length. 

Apparatus. — (a) The pendulum is made of a bullet 
of about 1.5 cm. diameter, into which is moulded a 
very small wire loop. A silk thread 120 cm. long 
is attached to this loop at one 
end, and passed into a knife slit 
in a cork near the other end. 

(5) By means of a screw 
clamp attached to a vertical rod, 
the cork is firmly supported so 
that the thread hangs perpen- 
dicular to the face from which 

it emerges. Fig. 1 3. — Showing how the 

^ k " pendulum is suspended. 

(c) A meter stick, a rectan- 
gular block and a pair of outside calipers (cf . Appen- 
dix B, Art. 3), are needed for measuring the lengths 
and the diameter of the bob. 

(d) For the time measurements a good timepiece, 
capable of marking seconds, is needed (e.g. a student's 
watch, a stop-watch, a metronome, or, best of all, a 
telegraph sounder, electrically connected with a good 
laboratory clock. 

Operations. — (a) Carefully measure the diameter 
of the bob. 

(6) Loosen the thumb-nut of the clamp, and draw 
the thread up or down through the slit in the cork, so 
as to make the pendulum between 25 and 50 cm. long. 



MECHANICS OF SOLIDS 59 

Tignten the nut, wind the thread around the cork, 
and pass it back through the slit, so it will not slip. 

(c) Measure accurately the distance D from the 

point of suspension to the bottom of the bob. 

To do this, lower the clamp till the surface of the table is 
tangent to the bob; and set the end of the rule against 
the table top. Or set the rule on end next the pendulum, 
rest a try square (or a draftsman's triangle, or a squared 
block) against the rule, sliding it up or down till its upper 
edge is in contact with the end of the thread or with the bot- 
tom of the bob, and then read on the rule the position of 
the square. 

(d) Lower the pendulum till the bob is near the 
table top; set it swinging over an arc not exceeding 
10°, and determine the period of a single oscillation 
as directed in Exercise 1, p. 1. 

(e) Without changing the length, determine the 
period as before for each of two different amplitudes 
smaller than the first. 

(f) Make the length between 50 and 75 cm. 
Measure it as before, and determine the period for 
three different amplitudes. 

((/) Repeat (f) but with length from 75 to 100 cm. 

Data and Calculations. — Tabulate the observed 
quantities as indicated on the following page. The 
real length /, in any case, is the distance D (cf . Op- 
eration c) minus R, half the diameter of the bob. a 
represents the amplitude, o the number of oscilla- 
tions made in s seconds, t the period (equal to — ), 

t 
and -j the ratio of the period to square root of cor- 
responding length (expressed as a decimal fraction). 



60 LABORATORY EXERCISES IN PHYSICS 



Numerical Data 





Length of 

Arc 

a 


Oscilla- 
tions 




Number of 

Seconds 

s 


Period 
t 


Ratio 
t 

\7 


D 












R 












I 












D 












R 












I 












D 












R 












I 













Sources of Error. — State concisely what errors may 
pertain to (a) the timepiece, (5) the observers, 
(c) the measurements of length. 

Inferences. — In complete sentences, answer the 
questions below. 

(a) Do your values of t corresponding to a given 
length, differ by amounts too great to be ascribed to 
the inevitable errors of the experiment ? 

(V) If not, when the length and place remain the 



MECHANICS OF SOLIDS 61 

same, is the period dependent upon the length of the 
arc.* 

(c) Do you consider it fair to assume that the 

values of - — are all equal, or, in other words, that 

/J is a constant ratio for all lengths ? 
(c?) If I and V be two lengths, and t and t r be the 
corresponding periods, and if — - = k (a constant 

quantity), and — = k also, show that — = . 

H yj VF t' VF 

(e) If you have answered (J) and (c) in the affirm- 
ative, state the two laws of the pendulum which 
you have verified by your experiments as far as they 
go. 

Part B 

ACCELERATION OF GRAVITY 

Purpose. — The purpose of Part B is to calculate 
the mean value of g at the school laboratory from the 
data obtained in Part A. 

Calculations. — (a) Put the equation of the pendu- 
lum, t = 7tv/-, into the form g = —> 

(J) In this formula, substitute 3.1416 for tt\ Sub* 
stitute for I the first value of length taken from the 
tabulated results of Part A. Average the values of 
the period of oscillation belonging to this length, and 

* Half the arc measures the amplitude of the oscillation, and 
theoretically it. should not exceed 6 , but practically it will be diffi- 
cult in this experiment to make it quite BO small. 



62 LABORATORY EXERCISES IN PHYSICS 

put the resulting quantity in place of t. Solve the 
equation for g. 

((?) In like manner, substitute and calculate the 
value of g from each of the other lengths and its 
corresponding mean period. 

QP) Tabulate and average these values of g to find 
the mean acceleration of gravity at your laboratory. 

(e) If given the theoretical value of g in your lati- 
tude by your teacher, find your error by subtraction, 
and calculate your percentage error. To do this, 
multiply your error by 100 and divide by the given 
.value of g. 

OPTIONAL PROBLEMS 

(a) Period-Length Graph. — Taking the values of I and 
the corresponding values of t from Exercise 18, represent the 
former by abscissas (scale: 1 cm. = 25 cm.) and the latter by 
ordinates (scale: 1 cm. =0.1 sec). Plot a graph. The first 
point of the graph (i.e., I = 0, and t = 0) will be at the origin. 
Label the parts of the graph, and tabulate the data as directed 
in Exercise 3. 

(6) Mass and Period. — Solder a pin to the bottom of 
a small covered lard pail (or stick it on with sealing wax, cf. 
Appendix H) . Attach a small vise to a wooden bracket on 
ths wall; and from the vise suspend the lard pail by a steel 
piano wire 2 or 3 meters long, so as to use it as a pendulum. 
A neater apparatus than the lard pail may be made out of 
a cylindrical tin box such as those in which varnish is sold. 
The screw top may be perforated, and the wire passed through 
it and soldered on the inside. Make a small pointer by stick- 
ing a knitting needle into a block of wood. After completely 
filling the pail with sand, put on the cover, and adjust the 
wire in the vise so that the point of the pin just meets the end 
of the pointer when the pendulum hangs at rest. Remove the 
pointer, and determine the period of the pendulum. Now sub j 
stitute water or iron filings for the sand; readjust the length 



MECHANICS OF SOLIDS 63 

if necessary, by means of the vise and with the aid of the 
pointer; and again determine the period. Since the equation 
for the pendulum 

contains no expression for mass or density, and is general pro- 
vided the amplitude is small, it implies that the period depends 
only on the length and the acceleration of gravity. Do you 
find that your experiments confirm this implication, i. e. that 
the period is constant for different masses and materials, pro- 
vided the length and place remain constant? 



CHAPTER II 

FLUIDS 

Exercise Number 19 
density of water 

References 
M & T 32 

The Purpose is to find the mass of one cubic centi- 
meter of water, i.e. the density of water. 

The Apparatus consists of a balance and weights, 
a cylindrical graduate, and a centigrade thermometer. 
Operations. — (a) Weigh accurately, a beaker or 
flask, containing approximately 200 cubic centime- 
ters of pure water; pour the water into an empty 
graduate, being careful not to spill any, and weigh 
the flask again. The difference between the two 
weights equals the mass in grams of the water now in 
the graduate. Why ? 

(b) Read the volume of the water by means of the 
scale of cubic centimeters on the graduate. fCf. 
Appendix C, Art. 2.) 

(<?) From the mass and the volume, calculate the 
density of the water. In the division discard all 
the figures beyond hundredths of a gram. With 
a thermometer, take the temperature of the water in 
centigrade degrees. On account of expansion due 
to the greater heat, the density of water at the tem- 

64 



FLUIDS 65 

perature of the room is slightly less than it would be 
at 0° C, its freezing temperature. 

Inferences. — The true value of the density of water 
at 20° C. differs from one gram per cubic centime- 
ter, but by a quantity less than half a centigram, 
which is less than your probable experimental errors. 
See how near your result comes to l^p. Is it near 
enough so that you may assume in most of your 
work that one cubic centimeter of water has a mass 
of one gram ? 

Exercise Number 20 

pressure in a liquid caused by its weight 
References 

A 150-152 GE 95-100 H&W128-130 

C 116-123 GP 122-128 L 157-167 

C & C 123-133 H 131-142 M & T 94-105 

W & H 63-71 

The Purpose is to learn whether a liquid exerts 
a pressure on a surface that is submerged in it, and 
to find in what way the pressure is affected by the 
depth. 

Apparatus.— A spring balance or an equal arm 
balance, mounted on a rod a that is supported by a 
screw clamp s which permits it to be raised or low- 
ered. From the pan of the even arm balance or from 
the hook of the spring balance a uniform rod r with 
squared ends is suspended by a silk thread, so as to 
hang vertically. The rod may be of aluminum (or 
of wood loaded with lead at the bottom, bo as to 



66 



LABORATORY EXERCISES IN PHYSICS 



sink upright in the water). The rod r is plainly 
marked with a scale of equal parts, and has a small 

wire loop in its 
upper end. A 
glass cylindrical 
graduate of say 
250 cubic centi- 
meters capacity 
is filled with 
enough distilled 
water so that 
when the rod is 
wholly sub- 

merged in it the 
water will rise 
nearly to the 250 
cc. mark. 

Operations. — 
(a) If the equal 
arm balance is 
used, balance the 
suspended rod 
with weights ; 
then lower the 
balance till the 
rod will be sunk 
Fi g- 14 - to the first of its 

division marks when the balance beam is horizontal. 
Does the water exert an upward pressure on the 
bottom of the rod ? How is it made evident ? Now 
remove sufficient weight from the pan to let the rod 




r 



FLUIDS 67 

sink till the beam remains horizontal. How does 
the lifting force at that depth compare with the 
apparent loss of weight ? May this apparent loss of 
weight be used as a measure of the upward pressure 
of the water on the bottom of the rod r ? 

(b) Lower the balance, and remove weight till the 
beam is again horizontal with the rod sunk to the 
next, division. Note the amount of weight removed, 
which represents the increase in the pressure of the 
water due to the increase in depth. 

(c) Continue this process until the rod is entirely 
submerged. Does the pressure now seem to in- 
crease, or does it seem to remain constant ? Do you 
suspect why ? 

(V7) If the spring balance is used instead of the 
equal arm balance, each difference between the bal- 
ance readings at two different depths is the apparent 
loss of weight and measures the increase in pressure 
due to the greater depth. 

Numerical Data.— Record the depths and cor- 
responding total pressures in two parallel col- 
umns. 

Graphical Representation.— Represent the relation 
of pressures to depths by a graph, plotting the lat- 
ter as abscissas and the former as ordinates. 

Inferences.— (a) From an inspection of the data 
and graph, state whether the increments (increases) 
of pressure are equal for equal increments of depth. 

(/>) If so state the law of the relation of pressures 
to depths. 

(<?) When the rod was just submerged, was there 



68 LABORATORY EXERCISES IN PHYSICS 

any water pressure upon its upper base ? What must 
have been the pressure on its upper base when sunk 
to a distance equal to one scale division ? The lower 
base was then one division deeper than before: why 
was the increased pressure on it not apparent ? Why 
does the resultant of the upward and downward 
pressures remain constant at all depths after the rod 
is once entirely submerged ? 

Sources of Error.— What sources of error did you 
find? 

OPTIONAL PROBLEMS 

(a) Sink a Hall pressure gauge (cf. Appendix F) to different 
depths in a battery jar of water. At each depth in succession, 
turn it around a vertical axis, and also (by means of the crank) 
around its horizontal axis, keeping the center of the diaphragm 
at the same level. Watch the drop of liquid in the horizontal 
indicator tube, and see whether it indicates any change of 
pressure on the diaphragm when the latter is turned in different 
directions without changing the depth of its center. State 
the law of the relation of pressure to direction of the sub- 
merged surface when the depth remains constant. 

(6) By means of a coupling and rubber tube, attach a small 
steam gauge to the water taps on different floors of the school 
building, record the pressures, measure the vertical distances 
between the levels of the taps, divide the increase of pressure 
between each two taps by the corresponding vertical distance, 
and see if the ratio of pressure to depth is a constant quantity. 
If so, state whether this experiment verifies the laws of liquid 
pressure with relation to depth and direction. 

(c) A cubic inch of water weighs 0.0361 lbs. Calculate the 
number of cubic inches in columns of water each 1 sq. in. in 
cross section and each having an altitude equal to one of the 
vertical distances between two taps. Find the weights of 
these columns, and compare them with the increments of 
pressure [in lbs. per sq. in. in Problem (b)] to which they cor- 
respond. 



FLUIDS 69 

Exercise Number 21 



THE PRINCIPLE OF ARCHIMEDES 


References 




A 153 GE 113 


H & W 112 


C124 GP146 


L 169-171 


C & C 134-137 H 143 


M &T 111, 112 


W & H 72-74 





Purpose. — It is proposed to find out how the buoy- 
ancy (lifting force) of a liquid on a body immersed 
in it compares in magnitude with the weight of the 
liquid displaced by it, i.e. to learn whether Archim- 
edes' principle may be verified by experiment. 

The Apparatus is that described in the preceding 
experiment. 

Operations. — (a) Repeat the experiment of sink- 
ing the rod to different depths till it is entirely sub- 
merged; but at each depth take a reading of the 
upper surface of the water in the graduate. Each 
time when more of the volume of the rod is sub- 
merged, the displaced water rises to a higher mark; 
and the difference between the two readings meas- 
ures in cubic centimeters the increase in the volume 
of water displaced. Since each cubic centimeter of 
water weighs one gram, the difference between two 
readings is also numerically equal to the weight of 
the displaced water. 

Data. — Record in two parallel columns the total 
buoyant force at each depth, and also the correspond- 
ing weight in grams of the water displaced. 

Inferences. — (#) State the principle of Archime- 
des, and say whether or not your results verify it for 



70 LABORATORY EXERCISES IN PHYSICS 

water, (b) Do you infer that it would be true for 
any fluid (i.e. for any other liquid or any gas)? 

OPTIONAL PROBLEM 
Special Case of a Floating Body. — Let the floating body 
be a rod of wood, or let it be a large test tube ballasted with 
shot, and having a paper scale of centimeters and millimeters 
pasted inside. For this case it should be loaded with only 
enough ballast to make it float upright and partly out of water. 
Weigh the body. Proceed as before with the experiment, 
comparing the buoyant forces with weights of displaced water, 
until the buoyancy has caused the rod apparently to lose all 
its weight. As long as the weight of the body is greater than 
that of the water displaced by it, what does it tend to do? 
When a body has sunk till the weight of water displaced is 
just equal to its own weight, what does it do? Push the 
body downward so the weight of water displaced by it is 
greater than its own weight, then release it. What does it 
do? A concise statement of its behavior is sometimes called 
the law of flotation. State this law. Does it apply to iron 
floating in mercury and to a soap bubble or balloon filled with 
illuminating gas and floating in air? Try it. Add five grams 
at a time to the ballast of the floating rod, and see each time 
if the new weight of the floating body and the weight of dis- 
placed water are equal. 

Another method of measuring the weight of the displaced 
water is that of having a vessel provided with a spout and 
filled up to the point of overflowing. W'hen the body is placed 
in the vessel, the overflow is caught and weighed. This method 
though apparently simple, is not uniformly accurate. 

Still another way of making the experiment is to suspend 
the filled vessel from the pan of an equal arm balance, and 
counterpoise it with sufficient weights. If then the floating 
body be lowered into it, just enough water will be displaced 
to leave the scales in equilibrium. This method, like the pre- 
ceding, is open to the objection that sometimes the overflow 
is greater or less than the amount actually displaced. The 
error is caused by surface tension a phenomenon in which the 
surface film of a liquid acts very much like an elastic skin 
which has to be broken before the liquid can overflow. 



FLUIDS 71 



Applications. — The weight of water that a ship displaces 
when as low in the water as it can safely be, is called its gross 
displacement. Weigh a toy boat, find its gross displacement 
by the overflow method, and calculate its greatest safe load. 
Test it with this load. Might a model be so used by a ship de- 
signer? How does an air ship, a fish, or a submarine boat rise 
or sink? 

Exercise Number 22 
relative density by the submersion method 

References 

A 153, 155, 156, 160 GE 114-116 H & W 59, 112, 113 

C 124 GP 146-149 L 169-176 

C & C 134-136, 140-144 H 143, 146-150 M & T 32, 111-113 
W & H 72, 73, 75 

Purpose. — The purpose of this exercise is to de- 
termine (a) the relative density of a solid and (J) the 
relative density of a liquid with reference to water as 
a standard. The solid chosen is to be denser than 
water or the liquid, and is to be insoluble in either. 
Under these conditions the methods are of general 
application. 

Part A 

OF A SOLID 

Apparatus. — The apparatus provided consists of 
balance and weights, thread, a jar or beaker of dis- 
tilled water, and the solid used in Exercise 0. 
Diagram the apparatus as used. 

Operations. — (a) Make a slip-noose at one end of 
the thread and a loop at the other end. 



72 



LABORATORY EXERCISES IN PHYSICS 



(6) Pass the loop over the hook * on the bottom of 
one of the scale pans, adjusting it to such a length 
that the solid, when suspended in 
the noose, will hang 10 or 15 cm. 
below the pan. 

(c) Adjust the scales to equilib- 
rium with the thread so attached. 

(6?) Suspend the solid, or place it 
in the pan, and obtain its weight, W. 

(e) Suspend the solid in the jar of 
water, adjusting the scales so that it 
is totally submerged when the beam 
is horizontal, but touches neither the 
sides nor bottom of the jar ; and 
obtain the apparent weight, W v 

(/) If time permits, suspend the 
solid from the other pan, and obtain 
the values of W and W 1 as before, 
using their mean values, as in Exer- 
cise 6. Ordinarily the arithmetical mean will do, 
because it does not usually differ from the geometric 
mean by an amount greater than that of the unavoid- 
able errors of experiment. 




Fig. 15. 



* If the balance pans have no hooks, the thread may be suspended, 
as shown in Fig. 15. If suspended in this way from the trip scales, 
the scales must be mounted on a box or other support, with the end 
of the balance projecting over the end of the box. The loop must 
be long enough so that the thread will not touch the base of the 
balance or any part of its support. A bit of soft wax will keep the 
thread in place. If the balances have the perforated horn pans, 
close the holes with corks and put small screw-hooks into the corks 
from below. 



FLUIDS 73 

Data. — Record data in the tabular form below. 

Numerical Data 



Substance of the solid 




Form of the solid 




Number of the solid 




Weight, W 




Apparent weight in water, W l 




Buoyant force, W — W Y 








w-w l 


Density from Exercises 6 





Part B 
OF A LIQUID 

Apparatus. — A jar of the liquid * whose relative 
density is to be determined is added to the apparatus 
of Part A. 

Operations. — The only additional operation is that 
of obtaining the apparent weight of the solid while 
submerged in the liquid under examination. 

Data. — Tabulate these as below, using the values 
of IF and W x obtained in Part A. 

* E.g. a saturated solution of common salt or of copper sulphate. 
Iron and lead cannot be used in the latter Liquid, as it acts upon 
them chemically. 



74 LABORATORY EXERCISES IN PHYSICS 



Numerical Data 



Substance of the solid 




Form of the solid 




Number of the solid 




Weight, W 




Apparent weight in water, W Y 




Buoyant force of water on solid, W — W x 




Apparent weight in liquid, W 2 




Buoyant force of liquid on solid, W — W 2 




JY — W 

Relative density of liquid, — -? 




Name of liquid 



Sources of Error. — These are as follows : (a) Im- 
perfections of the balances and weights. 

(6) Parallax in observing the pointer of the scales. 

(e) Friction of the liquid on solid and thread, 
reducing the sensitiveness of the balance. 

(d) Buoyant forces of the liquids on the thread. 
In very accurate work a silver or platinum wire is 
used, and corrections are made for the buoyant forces 
on it. 



FLUIDS 75 

(e) Buoyant force of air on the solid. When great 
accuracy is sought, the corrections for deducing the 
weights in a vacuum are applied. 

(f) Water may not be pure and at 4° C. Cor- 
rections for temperature may be applied. 

Inferences. — (a) If, by definition, 

.~ . _ Mass of the body 

Volume of the body 5 

may the numerical value of this ratio be obtained by 
taking the numerical value of the expression 

Mass of the body ^ ™ „ 

Buoyant force of water on the body' 

(b) If, by definition, the density of a liquid 

Mass of the liquid 
Volume of the liquid' 

may the numerical value of this ratio be obtained by 
taking the numerical value of the expression 

Buoyant force of the liquid on a solid 



Buoyant force of water on the same solid' 



Why? 



(c) Is the numerical value of the relative density 
the same as that of the density in grams per cubic 
centimeter i Why ? 

Practical Applications. — The density of a substance 
is one of its most important characteristics. The 
knowledge of it is often Indispensable, not only to 
the scientist, but also to the manufacturer, merchant 
and consumer. Find some instances. 



76 



LABORATORY EXERCISES IN PHYSICS 



Exercise Number 23 



RELATIVE DENSITY BY THE FLOTATION METHOD 



References 



A 154, 157, 160 


GP150 


L 172, 174, 177 


C & C 138-144 


H 144, 150 


M & T 111, 112 


GE117 


H & W 113 


W & H 74, 75 



Purpose. — In this exercise it is proposed (a) to 
determine the relative density of a wooden rod by 
applying the principle of flotation, 
and (5) to determine the relative 
density of a liquid by using the 
rod as a constant weight hydrom- 
eter. 

Apparatus. — (a) The rod of 
wood whose relative density is to 
be found must be of uniform cross- 
section, and should be given a thin 
coating of paraffin, so that it cannot 
absorb the water or other liquid. 

(6) A supply of distilled water 
and of the liquid, each in a tall 
glass jar. 

(e) A support for floating the 
rod upright consists of a piece of 
a meter rule, with two screw-eyes 
set horizontally into the front of 
it. A spring clamp attached to the 
back of it holds it firmly against FlG - 1 6.— Showing 

.,.,"-.,"■ the rod and support 

the side ot the jar. in position. 




FLUIDS 77 

Part A 
OF A SOLID 

Operations. — (#) Place the support vertically in 
the jar of water, and see that the clamp holds it 
firmly in position. 

(J) Pass the rod vertically downward through 
both screw-eyes, and carefully allow it to sink just 
as far as it will. Tap very gently on the side of the 
jar, or support, in order to overcome any friction that 
may interfere with free motion of the rod upward or 
downward. 

(c) Take two readings, on the support, of the 
position of the lower end of the rod, and the same 
number of readings of the upper level of the water. 
Wipe the rod dry, reverse it and repeat, taking four 
readings as before. Take the mean of the four 
readings for the lower end, and also the mean of the 
four readings for the water level. Avoid parallax 
by keeping the eye on a level with the point at 
which the reading is taken. If the surface of the 
water is elevated by capillary action near the rod, 
give the rod a fresh coat of paraffin. 

(d) With a metric rule take four measurements 
of the total length of the rod. 

Data. — Enter the data in a tabular form like that 
below. The length of the part submerged is obtained 
by taking the difference between the mean upper 
and mean lower readings. The relative density of 
the wood is calculated by dividing the length of the 
part submerged by the length of the entire rod. 



78 



LABORATORY EXERCISES IN PHYSICS 



Numerical Data 





Beading 
Lower End 


Reading 
Water Surface 


Length of 

Submerged 

Part 


Length of 
Entire Rod 


1 










2 










3 










4 










Mean 










Name of substance 




Relative density 





Theory. — Let W= weight of rod, m its mass, I its 
length, and V its volume ; let W 1 = weight of water 
displaced by submerged part, w! its mass, v' its vol- 
ume, V its length (i.e. the length of the submerged 
part of the rod); and let D be the density of the 
substance of the rod, D f the density of water, and a 
the cross-sectional area of the rod. 

Then W= W (Principle of Flotation) ; and since 
W = m, and W r = m' (mass is numerically equal to 
weight when expressed in gms.-wt.), 

m = mf (Why?) 



FLUIDS 79 

Also m = VD and m! = V'D f ; 

... VD=V f D r . (Why?) 

But V= al and V f = aV . (Geometry.) 

Whence, by substitution, 

alD = aVB ! ; 
and dividing by alD\ 

D V 
Relative Density = — =—. 

Evidently this method applies to any substance 
less dense than water, provided it be cut of uniform 
cross-section, with its bases approximately perpen- 
dicular to its length. 

Part B 

OF A LIQUID 

Operations. — (a) Wipe the rod and support 
(Why?), and repeat operations (a), (£), and (c?) 
of Part A, but with the rod floated in the liquid 
whose relative density is to be determined instead 
of in water. 

In a tabular form like that on the following page 
enter the data thus obtained, together with the nec- 
essary datum from Part A. 

(J) Calculate the relative density by dividing the 
mean length of the part submerged in nutter by the 
mean length of the part submerged in the liquid, in 
accordance with the theoretical deduction, p. 80. 



80 LABORATORY EXERCISES IN PHYSICS 



Numerical Data 



Trial 


Reading 
Lower End 


Reading 
Liquid Level 


Length of 
Part Submerged 


1 








2 








3 








4 








Mean 








Length of part submerged in water 




Relative density of liquid 




Name of liquid 





Theory. — Let TF, M, V, a, and I represent, respec- 
tively, the weight, mass, volume, sectional area, and 
length of the displaced liquid; and let W\ M f , V, 
a, and V represent, respectively, the same quantities 
for the displaced water. Also let D and D ! be the 
densities of the liquid and of water. 

Then W— W 1 (since by the Principle of Flotation 
each is equal to the weight of the rod) ; and by rea- 
soning precisely similar to that of Part A, 



— = y = Relative Density of the Liquid. 



I 



FLUIDS 81 

Sources of Error. — Errors result from (a) parallax, 
and errors of judgment in reading (personal equa- 
tion). (J) The rod and support may not be exactly 
vertical, (e) Slight friction may prevent the rod 
from floating freely. (d) The rod may not be 
exactly vertical. 

Lessons. — This exercise gives valuable practice in 
manipulation, and in the application of the principle 
of flotation for the rapid determination of density 
where refined methods are not available. It also 
illustrates the principle which underlies all constant 
weight hydrometers. 

The Principle of Flotation is fundamental in ship 
designing. The weight of a vessel equals its " dis- 
placement." A battleship designed to carry heavy 
armour and heavy guns must have a large displace- 
ment and great stability. This necessitates increased 
draught and breadth of beam. The naval designer 
must compromise between weight and speed. Com- 
pare a protected cruiser with a first-class battleship. 

Additional Work. — Other woods and other liquids may be 
given, if desired. 

Note. — If the support is not at hand, the rod may be sup- 
ported laterally by the ringer tips. A ring of fine silk thread 
may be adjusted on the rod to mark the upper level of the 
liquid, and the length of the part that was submerged measured 
by a rule. Paraffining the rod and support serves the additional 
purpose of preventing the Liquid from adhering to them, and 
thus disturbing the true level of the liquid. It is desirable to 
use the same liquid that was chosen for Exercise 22, so that the 
results by the two methods may be compared, and a check on 
their accuracy thus secured. 



82 



LABORATORY EXERCISES IN PHYSICS 



Exercise Number 24 
relative density of a liquid by hare's method 



A 165, 166 
C 131-133 
C & C 146-148 
GE 102-104 



References 

GP 131, 144, 149 
H pg. 139, 159-161 
H & W 121, 153 
L182 



M & T 97-100 



Purpose. — The purpose of this exercise is to deter- 
mine the relative density of a liquid by the method 
of balancing columns supported by atmospheric 
pressure. 

Apparatus. — The apparatus consists of two glass 
tubes, each nearly a meter long, and joined by rubber 
tubing to the two branches of 
a three-way tube (made from a 
T-tube bent as shown) ; and to it 
is attached a long rubber tube 
terminating in a glass mouthpiece. 
The glass tubes are secured to a 
meter stick by rubber bands, and 
the meter stick is fastened in a 
vertical position by screw clamps 
(or by any convenient support). 
Its end rests on the table-top. 
The ends of the glass tubes should 
terminate in short rubber tubes 
which dip into two beakers or small 
jars, one containing distilled water, and the other the 
liquid whose relative density is to be determined.* 

* Use the same liquid as in Exercises 22 and 23. 




Fig. 17.— Appara- 
tus for the determina- 
tion of relative density 
by Hare's method. 



FLUIDS 83 

A pinch-cock, or a Hoffman screw-compressor, is 
placed above the mouthpiece on the rubber tube, to 
prevent the ingress of air after it has been withdrawn. 

Operations. — (a) Remove, rinse, and replace the 
mouthpiece. 

(5) Open the pinch-cock, remove air from the 
tubes until the columns of liquid stand a little below 
their upper ends. 

(Why do the liquids rise to unequal heights? Which liquid 
is the denser?) The air is to be removed by suction at the 
mouthpiece a little at a time, so as never to allow the liquids 
to be pushed over the bend. (Why?) In case such an acci- 
dent should occur, remove the entire apparatus to the sink and 
rinse it thoroughly. The columns can be held at any desired 
point, while the pinch-cock is being adjusted, by closing the 
end of the mouthpiece with the tongue. 

(V) After closing the pinch-cock, watch the appara- 
tus for a moment, to see that it does not leak, then 
read on the rule the positions of the upper ends of 
the columns. Read to tenths of millimeters, being 
careful to avoid parallax. In like manner read the 
position of the liquid surface in each of the beakers. 
Make each upper and each lower reading from the 
bottom of the meniscus. In reading, it is convenient 
to hold a straight-edged card against the scale and 
tube, with its upper edge parallel to the divisions of 
the rule. The two lower readings should be taken 
as nearly as possible at the same instant, and so also 
should the two upper readings. 

(d) Let the liquid columns run down a few cen- 
timeters, and repeat the observations. Take as many 
sets of readings as time permits. Remember that 



84 



LABORATORY EXERCISES IN PHYSICS 



the longer the columns, the less is the percentage 
error. In order to eliminate the small error due to 
capillary action, it is well to have a short piece of 
tubing, like that of the apparatus, placed in each 
beaker, and to take each lower reading at the bottom 
of the meniscus in the short tube. This tube should 
be held vertically, and not too near the long tube or 
to the side of the beaker. 

(e) Remove the pinch-cock after completing the 
readings. 

Data and Calculations. — Record the name of the 
liquid, the readings, and the derived data in a tabu- 
lar form like that below. The height of each col- 
umn is obtained by subtracting the smaller reading 
from the greater. The relative density for each set 
of readings is obtained by dividing the height of the 
water column by the height of the liquid column. 
Compute the mean relative density from the num- 
bers in the last column, and record it below the data, 
together with the values of the relative density of 
the same liquid obtained in Exercises 22 and 23. 

Numerical Data 



Water 


Liquid 


Lower 
Reading 


Upper 
Reading 


Height of 
Column 


Lower 
Reading 


Upper 
Reading 


Height of 
Column 


Relative 
Density 

















FLUIDS 85 

Theory. — Let m, v, a, A, and D represent respec- 
tively the mass, volume, sectional area, and height 
of the liquid column ; and let m f , v f , a, h 1 ', and 
D f represent the same quantities for the water 
column. 

Then since they are balanced by the same result- 
ant atmospheric pressure, the weights and there- 
fore the masses of the two columns are equal, i.e. 
m = m f . 



But 


m = vD — 


aliD 






and 


to' = v'D' = 


= ah'D'. 




(Why?) 




.-. ahD = ah'D' 


3 




(Why?) 


and 


hD = h'D'. 






(Why?) 


Whence 


D h' „ , ,. 
-j-=— = Kelative 


Density 


T. (Why?) 



I)' h 

Sources of Error. — (a) Errors may arise from 
temperature changes. In very accurate work cor- 
rections must be applied for expansion ; or the col- 
umns must be cooled to 4° C. 

(J) Dirt in the tubes may affect the amount of 
capillary elevation or depression. 

(V) There will also be errors due to parallax and 
personal equation. 

Lesson. — Besides useful laboratory practice this 
exercise affords valuable practice in applying the 
principles of fluid equilibrium. 



86 LABORATORY EXERCISES IN PHYSICS 

Exercise Number 25 
calibration and use of a lactometer 

References 
\ 154, 160, 161 GE 113-117 H & W 112-116 

C 121-124 GP 146-151 L 169-172,177-178 

C & C 138, 139, 144 H 143-150 j M & T 112 

W & H 72-75 

The Purpose is to graduate a glass tube so as to 
use it for determining the density of any given 
liquid sucli as milk, and to see how density indicates 
the purity. 

The Apparatus consists of a deep glass jar and a 
"blank" hydrometer-tube. This is a slender glass 
tube, open at the upper end, and having two bulbs 
blown in it, — one at the lower end, and the other a 
few centimeters above the first. A Bunsen burner, 
a paper millimeter scale, balance and weights, dis- 
tilled water, salt, some mercury or fine shot, and a 
bit of sealing wax are also provided. 

Construction. — (a) First insert cautiously some 
mercury from a small paper funnel, or some shot, 
as ballast till the tube floats upright in a jar of dis- 
tilled water, and is submerged to within two or 
three cm. of the upper end of the tube. With a 
long wire push a bit of cotton into the neck of the 
bulb to act as a stopper. 

(b) Trim the millimeter scale till its width is a 
little less than the inner circumference of the tube; 
then roll the scale sidewise round a small glass rod 
or tube so as to make of it a cylinder; and slip it, 
zero end up, into the tube. 



FLUIDS 87 

(c) Again float the tube in the water; and with a 
stiff wire move the scale up or down until the zero 
coincides with the water level. Test it carefully to 
see if it is right, then fasten it in place by means of 
a tiny bit of sealing wax (which you can melt with a 
hot wire). After floating the tube again to see if 
the zero is correct, the open end may be fused in 
the Bunsen flame and closed with a pair of pincers, 
— care being taken not to remove any of the glass. 
Why 1 

Calibration. — (a) Thoroughly dissolve 2.50 gm. 
of salt in 250 cu. cm. of distilled water, thus 
making a solution of brine having a density of 1.01. 
Immerse the tube in this solution, and take the 
scale reading to which it sinks. 

(b) Add another 2.5 gm. of salt to the water, stir 
till thoroughly dissolved, and again immerse the 
tube and take the reading. 

(c) Continue this process until no more salt will 
dissolve in the water. If it is desired to carry the 
calibration further, barium chloride or lead acetate 
(Caution! They are both poisons) may be used, as 
these substances are much denser than salt, and 
therefore denser solutions may be obtained with 
them. 

Calibration Graph. — Plot a graph using the scale 
readings as abscissas, and representing the corre- 
sponding densities by ordinates on any convenient 
scale. 

Density of an Unknown Solution. The teacher 
may have prepared several samples of brine (called 



88 LABORATORY EXERCISES IN PHYSICS 

A, B, C, etc.), whose densities are known to him 
but unknown to the members of the class, (a) 
Place the instrument, which will now be called a 
hydrometer, into one of these solutions; take the 
scale reading and from the calibration graph deter- 
mine the density of the solution, (i) To do this, 
find the point on the axis of abscissas that corre- 
sponds to the observed scale reading, and erect 
there a perpendicular cutting the graph, at a point 
which may be designated by the letter of the solu- 
tion tested, (c) Measure the length of this perpen- 
dicular from the axis of abscissas to the point of the 
graph. This distance multiplied by the number of 
grams per cubic centimeter that one cm. represents 
on the axis of ordinates is the density of solution 

111 cms- 

Lessons. — (a) State why the hydrometer rises in a 
solution denser than water. (b) State how you 
would calibrate a hydrometer to be used for liquids 
less dense than water. 

The Sources of Error are, changes in temperature 
of the water or solution, and errors in reading the 
scale. The scale should be read as accurately as 
possible, — to five-tenths of a millimeter at least. 
Avoid parallax. 

OPTIONAL PROBLEM 

Milk Test. — A hydrometer used for testing the density of 
milk is called a lactometer, (a) Bring from home a sample of 
your milkman's milk. Stir the cream into the milk, and test 
the density of the sample with your hydrometer, as you did 
that of the salt solution. It should be between 1.030 and 



FLUIDS 89 

1.033. (b) Think out how the density of milk would be 
changed by watering it, then water a part of it and see if your 
prediction is verified, (c) Since the cream is buoyed up by 
the milk so that it floats to the top, do you infer that it is 
more dense or less dense than skim milk? Should the milk 
be more dense or less dense when the cream is stirred into it 
than it is when the cream has been separated from it? Test 
a sample of the milk from which the cream has been skimmed, 
and compare its density with that of the unskimmed milk. 
State- whether or not your conclusion is verified by the test. 
Dishonest milkmen sometimes skim their milk, and then add 
water till the gain in density due to the removal of the cream 
is offset by the loss due to the dilution with water. This fraud 
may be detected by determining the percentage of cream in a 
sample of the milk, and this will be found too small. 

In the Babcock Cream Test, a sample of the milk is placed 
with sulphuric acid in measured proportions in a specially 
graduated flask. Considerable heat is generated by the chem- 
ical action which results; and all the other constituents are 
separated chemically from the cream. The cream, however, 
still remains mechanically mixed with them. The flask is 
then placed with four others in a whirling apparatus, and 
rapidly revolved (with their bottoms outward toward the 
circumference of the circle of revolution) for several minutes. 
On account of its smaller density the cream is pushed inward 
toward the center of the circle of revolution by the denser 
milk residues and so collects in the long graduated neck of 
the flask, while the other constituents press outward toward 
the circumference, i.e. toward the bottom of the flask (cf. 
M. & T. Art. 89-91). When the flask is removed from the 
separator the amount of cream can be read off in the graduated 
neck of the flask. 

Besides the heat of combination of sulphuric acid and water, 
this test shows the effect of centrifugal force with rotation, 
for the cups in which the flasks are held hang vertically :it 
first, but stand out horizontally when rotated. It also demon- 
strates the necessity of balancing the moments of mass (cf. 
M & T, Art. 89-93); for there must be either two or four 
flasks placed symmetrically in order that they may rotate 
smoothly. 



90 



LABORATORY EXERCISES IN PHYSICS 



Exercise Number 26 



CONSTRUCTION AND USE OF PUMPS 
References 
A 172-175 GE 109, 111 

C 135 GP 144, 145 

C &C 159-160 H 171, 177 

W& H 84-87 



H & W 142-147 
L 182 

M & T 94-99, 101, 
102, 110 



Construction. — The parts of a model pump, Fig. 
18, may be made by the student or teacher at prac- 




Pr 



i!P 



Iv 



< i • 
* i i 

! » ' 



i>^rt£ = ^ 



Fig. 18. 

tically no cost. The cylinder O is made by cutting 
off squarely the end of a broken test tube (cf . Ap- 
pendix F). This end is thickened in a Bunsen 
flame, and made flaring, like the other, to receive 
the bottom B. B is a cork, perforated to receive a 
piece of glass tubing Ip about 15 cm. long. I p 



FLUIDS 91 

represents the inlet pipe. The inner end of the 
inlet pipe is covered by the inlet valve I v cut from 
a piece of dentist's sheet rubber, and stuck on with 
a short pin,jp r The piston Pis a cork, filed to a 
cylindrical form so as to fit £7 snugly, but not tightly 
enough to stick. It is perforated to receive the pis- 
ton rod P r. This rod is keyed into the cork by a 
pin- or a peg, p 2 . Another perforation is covered 
by the outlet valve v, made and mounted just as 
I v is. 

Operation.— Observations. — Answer the questions 
by clear concise sentences, so as to make a descrip- 
tion of the action of the pump and of its theory. 
Make a diagram from the apparatus itself, and refer 
to it in your description. Do not use the word 
suction* 

(a) Assemble the parts as shown, place the bottom 
B firmly in the lower end of the cylinder (7 and push 
the piston P into the upper end of C. Place the 
end of the inlet pipe Ip in a battery jar of water. 

(Jj) Push down the piston rod Pr, and watch the 
valve i\ Probably you cannot see it lift. Prime 
your pump by pouring in a very little water at the 
top. Now work the piston up and down. Which 
valve opens, and which one closes during the down 
stroke ? What pressure closes the one and opens 
the other? Of what two pressures is this pressure 
the resultant \ What becomes of the air that was in 
the cylinder during the first down stroke i During 
the next up stroke I What becomes of the air in 
the inlet pipe during the first up stroke 1 What 



92 LABORATORY EXERCISES IN PHYSICS 

finally happens to all the air that was in the cylinder 
and inlet pipe ? 

(c) Continue raising and lowering the piston. 
Watch the valves and the incoming and outgoing 
water at each stroke. What resultant pressure 
closes the inlet valve and opens the outlet valve on 
the down stroke? What resultant pressure keeps 
the outlet valve closed during the up stroke ? What 
resultant pressure opens the inlet valve at the same 
time ? 

(d) How does priming a pump cause it to work 
better? 

(e) Read the barometer (cf. Appendix E), so as 
to find how high a column of mercury the atmos- 
phere is supporting; and remembering that the den- 
sity of mercury is 13.6 |^- 3 , while that of water is 
1 J^p, calculate how high a column of water the 
atmospheric pressure would support in the inlet pipe 
of a pump, provided the pump did not leak. Sup- 
pose that the inlet pipe were longer than this and 
you worked the pump: what would happen ? Why ? 

OPTIONAL PROBLEMS 

(a) Suction. — The word suction means a process, not a 
force, and is a convenient word when so used; but ignorant 
people often talk glibly of a "force of suction," and about 
"drawing" or "pulling" water or air out of places, thinking 
they are explaining something. Make the following experi- 
ment, and then say whether there is any such thing as a force 
of suction. Remove the piston from the pump; and leaving 
the inlet pipe in the water withdraw the air from the cylinder 
by the process of suction with the mouth. Note that in doing 
so you simply enlarge the mouth cavity, thus reducing the air 



FLUIDS 93 

pressure in it and the cylinder. Do you thus exert on the 
water a force of suction which pulls or draws it up? Or is the 
water simply pushed up by something else? By what? Xow 
place your finger over the lower end of the inlet pipe, so this 
push from without cannot be exerted on the water within the 
pipe; and suck again at the mouth of the cylinder. Can you 
pull the water up? Is there a force of suction? 

(6) A Force Pump may easily be made similar to the lift 
pump. In this, the piston P is solid; and the lower cork B 1 
has two holes, one fitted with the inlet pipe and inlet valve, 
and the other fitted with a U shaped outlet tube Ot 
(cf. Fig. 18). This outlet tube passes from below through the 
cork of an inverted flask Ac which will serve as an air chamber. 
The outlet valve Ov 2 is placed over the end of the outlet tube 
inside the air chamber. Through the cork of the air chamber 
another glass tube is passed to which is attached a piece of 
rubber tubing and a small glass jet, representing a hose and 
nozzle. Operation: work the force pump, watch the motion 
of the valves and liquid, and also of the air in the air chamber. 
May the description of the action and theory of the lift pump 
be applied to explain the force pump, with very slight changes? 
What changes if any? What is the use of the air chamber, 
which may be seen on almost all force pumps? 

(c) The Siphox. — Fill a rubber tube about 18 inches long 
with water, close the ends with your fingers, and invert it 
with one end in a jar A of water and the other in an empty 
jar B at a slightly lower level. Remove the fingers. Docs 
the water flow from the higher jar into the lower? When the 
lower jar is about half full raise it till the 4 water levels are the 
same in both jars. Does the water flow now? Raise B till 
the water in it is at a higher level than that in .1. Which way 
the water go? Determine the rate of flow. i.e. measure 
the number of em.'' that flow out in a certain time and divide 
t he former by t he latter. 

Increase the difference of evel between the water surfs 
in the two jars, so a- to make the long arm of t he siphon still 
longer. What Istheeffecl nut he rate of flow? With the help 
of Problem 13, and Fig. so. Maim & Twiss'e Physics, p. 135, 
state briefly the behavior of the siphon under the conditions 
just mentioned, and explain why it so ac 



94 



LABORATORY EXERCISES IN PHYSICS 



A 168, 169 
C 136-142 
C & C 161-163 
GE 107 



Exercise Number 27 

boyle's law 
Part A. — Verification 

References 

GP 131, 137 
H 166-168 
H & W 124, 125 
L 189-190 



M&T114,115 
W & H 79-81 



Purpose. — The purpose of this exercise is to deter- 
mine the relation between the volume 
of a given mass of gas, at constant 
temperature, and the pressure under 
which it is confined ; or, more briefly, 
it is to verify the law of Boyle. 

Apparatus. — (a) A glass tube about 
30 cm. long, closed at one end by a 
capping disk and clamp screw, is joined 
by about a meter of rubber gas tubing 
to another glass tube of the same bore, 
open at both ends and about 50 cm. 
long. This composite tube is mounted 
on a board so that the two sections of 
glass tubing are vertical, and can slide 
up and down on opposite sides of a 
meter rule. They are suspended by 
a cord, sliding over screw hooks at the 
top of the board, and can be held in 
position by stiff rubber bands. The fig. 19. — Ap- 
apparatus contains as much mercuiy paratus for ver- 
as will fill it to the middle points of Law* 



FLUIDS 95 

the two glass sections when these points are at the 
same level. 

This adjustment should be made by the teacher (or, if by a 
student, under the eye of the teacher) as follows : (1) Set the 
tubes so that the middle points of the glass sections are at the 
same level. (2) Torn the clamp screw backward, and loosen 
the capping disk so as to allow free passage of air under it. 
(3) Pour mercury through a funnel into the open section till it 
stands at the middle points of the two glass sections. (4) Ad- 
just the capping disk, and force it down by the clamp screw till 
it closes the tube air-tight. The board is secured to the table 
in an upright position by screws, or by clamping in a vice or 
carpenter's hand-screw. 

(£) A mercurial, or aneroid barometer, and a 
thermometer are provided. 

Operations. — (a) Note the temperature of the air 
near the apparatus. It should be kept constant 
throughout the experiment. 

(6) Adjust the open tube at the greatest conven- 
ient height, and the closed tube at the least. Read 
and record the following : (1) The height of the 
barometer, B, in cm. ; (2) the level, s, of the 
mercury in the open tube; (3) the level, s ! , of 
the mercury in the closed tube ; (4) the level, e, of 
the upper end of the air column inside the closed 
tube. Read from the middle of the meniscus, esti- 
mating, if practicable, to the hundredth of a centi- 
meter. 

(c) Lower the open tube and raise the closed tube 
each a few centimeters, and take a new set of four 
readings as before. 



96 LABORATORY EXERCISES IN PHYSICS 

(d) Continue the process until the open tube is at 
the lowest convenient point, and the closed tube at 
the highest. Obtain one set with the mercury at the 
same level in both tubes. 

Data and Calculations. — Let a represent the inter- 
nal sectional area of the glass tubing, I (= e — s'), the 
length of the column of confined air, and h (= s — s f , 
positive or negative), the difference of level between 
the two mercury surfaces. 

(a) Record in tabular form, making a column for 
the different values of each of the following quan- 
tities : «, s\ e, I, h, B, B + h, (B + K) x I. 

(b) State whether the values of (i? + h) xl are 
equal within the limits of experimental errors for all 
values of B + h and the corresponding values of I ; 
i.e. is the product (5 + A) x I a constant ? 

If the sectional areas of the tubes are uniform, 
the volume T^of the confined air varies as Z, and the 
total pressure is P—B-\-K (For P equals the 
weight per sq. cm. of the mercury column Z, plus 
the weight per sq. cm. of the atmosphere on the 
mercury in the open tube; and this atmospheric 
pressure is measured by B.) 

Therefore if (B + h) X I is found to be constant, 
VP must be constant. Hence we may write for a 
given mass of gas at constant temperature, 

— VP— K (K being some constant), 

or VP = V P', 

V P f 

° r ' P = P • 



FLUIDS 97 

Inference. — (a) Write a general verbal statement 
of the meaning of the equation, VP = K, and also of 

V P ! 

the meaning of the equation, — ■ = — . 

(6) Do your results verify these two statements ? 

Sources of Error. — These are : (a) Any cause tend- 
ing to change the temperature of the confined air or 
mercury. Hence, avoid letting the hands, the breath, 
or sunshine come into contact with them. 

(J) Parallax. 

((?) Air or other impurities mixed with the mer- 
cury. 

(tT) Leakage, inward or outward, changing the 
mass of confined air. This will not occur if the 
capping disk is tight and the rubber tube is securely 
wired and cemented to the glass tubes. 



PART B. OPTIONAL PROBLEM 

Pressure-Volume Graph. — Represent observed values of 
/ by abscissas, and corresponding values of B-\- h by ordinates. 

Since the values of B-\-h are rather large in proportion to 
the amounts by which they differ from one another, it is well 
before plotting to subtract from each ordinate an even amount 
(say 50 cm.) somewhat less than the smallest observed value of 
B-\- h; or in other words to let the base line of the graph rep- 
resent B-{-h = 50 cm. instead of the axis of abscissas, which 
represents B-\- /i = 0. 

This leaves the lower ends of all the ordinates off the page, 
but does not cut off any points of the graph that represent 
observed values of B-\- h. 11* this is done a larger scale can be 
used, say for B -f- h 1 cm. = 5 cm. and for I (if the left ends of 
the abscissas arc also left off), 1 cm. = 1 cm. 

From the changes of slope of the graph infer the limit of V 
when P approaches (1) zero, and (2) infinity. 



CHAPTEK III 



HEAT 



Exercise Number 28 

changes of temperature and of state 

References 



A 216-221, 235, 240 

C 131-133, 220-223, 229-232, 

243-245 
C & C 305-315, 331, 337 
GE 126-128, 145, 149, 150 
GP 206-214, 239, 248, 262 



H 235-245, 272, 274, 277, 286 
H & W 121, 167, 168, 177, 

184, 186, 187 
J 1-9, 12, 41-43, 47, 50-54, 56 
M & T, 116-137 
W & H 90, 94, 99, 102, 104 



The Purpose is to study some of the phenomena 
of melting and boiling. 

The Apparatus consists of a 
centigrade thermometer, a tin 
cup (or a beaker), a boiler Fig. 
20, a Bunsen burner, and a 
U-shaped open mercury gauge, 
Fig. 21. 

Operations. — Observations. — 
(a) Nearly fill the tin cup with 
cracked ice and fill the inter- 
stices between the lumps of ice 
with cold water. Make a hole 
for the thermometer with a 
pointed stick, and push it cau- 
tiously into the hole till it is submerged up to 
the zero mark. Watch the mercury. Does it 

98 




CUP 



SCREW-CAP 
Fig. 20— The Boiler. 



HEAT 99 

descend ? Stir the ice and water frequently with 
the stick, being careful not to break the thermom- 
eter. After a time do you find that the mercury 
becomes stationary ? If so, take the reading to 
tenths of a degree. While reading the thermometer 
allow only the upper end of the mercury column to 
emerge from the water. Prefix the positive (+) 
sign if this reading is above zero or the negative 
(— ) sign if it is below zero. This reading is the 
zero error of the thermometer, and must be sub- 
tracted algebraically from any reading of this ther- 
mometer in order to get the correct temperature 
with it. 

In reading avoid parallax by keeping the line of light per- 
pendicular to the scale at the point of reading. The divi- 
sions will look straight when read from the correct position, 
but will appear convex downward or upward if the eye is too 
high or too low. 

(b) Place the cup on a retort ring (over asbestos 
or a sand bath if the beaker is used). Turn on the 
gas and ignite it by holding the lighted match at 
least four inches above the burner. If the flame 
"strikes back n arid burns in the tube, turn off the gas 
and relight it. 

Now place the lighted burner under the cup, and 
stir the mixture of ice and water continuously, 
watching the thermometer till the ice is all melted. 
Poes the temperature remain constant during this 
time? This constant temperature is called the melt- 
ing point of ice. Do butter, paraffin, beeswax, 
lead, etc., have the same melting point as ice I 

(c) Watch the thermometer after the ice has 

L OF C. 



100 LABORATORY EXERCISES IN PHYSICS 

melted. Does the temperature change ? Does it rise 
steadily with the steady addition of heat, or does it 
change suddenly? 

(d) Transfer the water to the boiler, screw on the 
tall vertical tube, close the overflow tube (but not 
the escape tube) with a wooden plug. Attach a 
T-shaped wire stop to the ring in the thermometer, 
and pass the thermometer through a snugly fitting 
cork which is to be placed in the end of the vertical 
tube. The thermometer will now hang in the water 
vapor, and will register its temperature. Watch 
the thermometer until the water is heard to boil and 
a steady cloud of condensed steam is seen at the 
escape pipe. What you see consists not of steam 
but of water in minute globules. Is steam visible ? 
(Look at the space between cloud and the opening 
of the escape pipe.) You may put your fingers into 
the cloud at some distance from the opening; but 
you will get badly burnt if you do not keep them 
out of the invisible jet of steam. 

(e) Can you increase the temperature of the steam 
by a more rapid supply of heat so long as the steam 
is escaping freely ? 

(f) If you are satisfied that the temperature 
remains constant, read the barometer, and then read 
the thermometer to the tenth of a degree, allowing 
only the upper end to emerge from the hole in the 
cork. Record the reading of the thermometer as 
the boiling point of water at the observed atmospheric 
pressure, and according to the thermometer you are 
usinq. 



HEAT 



101 



(g) Remove the plug from the overflow tube and 
attach the mercury gauge (Fig. 21) by means of a rub- 
ber tube. Does the mercury 
remain at the same level in 
both arms of the gauge ? If 
so, how does the pressure of 
water vapor at the boiling 
point compare with the sur- 
rounding {i.e. the atmos- 
pheric) pressure ( 

(h) Turn down the gas, 
close the escape pipe by 
means of a rubber tube and 
pinch cock, then cautiously 
increase the heat if neces- 
sary, thus causing both the 
temperature and the pressure 
of the vapor to rise. Take 
readings of several temper- 1 
atures and corresponding Fig.21. 

pressures. The pressures are read in millimeters of 
mercury by observing the number of mm. by which 
the mercury column on the air side of the gauge 
exceeds that on the vapor side. This excess added 
to the barometric reading gives the total pressure 
on the confined vapor < of. Exercise 27 p. 96). Does 
an increase in the surrounding pressure raise the 
boiling point? Why should it do <o( 

Turn oil' the gas and watch the changes of 
pressure as the teniperat urc falls. Watrh particu- 
larly for the point when the total pressure equals 




102 LABORATORY EXERCISES IN PHYSICS 

760 millimeters. Your thermometer, if correctly 
graduated, will then read 100°. Is it correct? If 
so, record the fact; if not, record the amount of the 
error. 

(j) After a time the temperature of the vapor 
will have fallen two or three degrees below 100°, 
and if the holler and connections are air tight, the 
excess of mercury will be on the vapor side of the 
gauge. Does this mean that the vapor pressure is 
less than that of the atmosphere ? Is the vapor 
pressure then equal to the barometric pressure 
minus this excess ? Why ? Does a decrease in the 
pressure cause a lowering of the boiling point? 
Why should it ? 

Numerical Data. — Record the observed numerical 
quantities in a neatly devised tabular form. 

Lessons. — The questions in the preceding section 
are intended to guide the student in his observa- 
tions and thought. He is expected to write under 
this heading in the fewest words possible a clear 
description of the observed phenomena. 

OPTIONAL PROBLEMS 
(a) Boiling Point Error. — Careful observations of the 
change of boiling point of water due to changes of pressure 
show that the boiling point increases 1° C. for every 27 mm. 
increase of pressure, or 0.037° per mm. How do your observa- 
tions compare with this statement? Then, if we wish to calcu- 
late the boiling point t° as indicated by a correct thermometer 
at any barometric pressure B, we may do so by adding to 100° 
0.037° for every millimeter by which the observed barometer 
reading exceeds 760 mm. (standard pressure), or sub- 
tracting from 100° 0.037° for every millimeter by which it is 
less than 760 mm. [In symbols t° = 100° + 0.037 (B-760).] 



HEAT 103 

Let the student calculate the true value of the boiling 
point at the observed atmospheric pressure, find the boiling 
point error, by subtracting algebraically the true boiling point 
at the observed pressure from that indicated by his thermometer 
and record this error with the other data and the number on 
the label of the thermometer. 

A thermometer whose errors amount to more than half a 
degree will not give respectable results in the experiments 
on specific heat and latent heat. 

(b) Melting Point of Tallow or Beeswax. — Heat a 
glass tube in the Bunsen flame, rotating it in the fingers till 
soft, withdraw it from the flame and quickly pull it lengthwise, 
making a thin tube. Break off a piece of this capillary tube 
about 6 cm. long. Melt some tallow or beeswax and suck up 
some of it into the tube, avoiding the admission of air bubbles. 
Fasten this tube to a thermometer with a small rubber band. 
Place them in a cup or beaker of water and heat the water, 
Stirring it meanwhile. When the substance begins to melt, 
H becomes transparent. When this occurs, observe the 
temperature. Now let the water cool, and when the substance 
solidifies and becomes opaque, take the temperature again. 
The mean of these two temperatures is the melting point of 
the substance. Is the melting point of a substance practically 
the same as its freezing point? 

(c) Determine the Boiling Point of Alcohol or ether 
by placing some in a test tube with a thermometer and heating 
it in a bath of water till it boils steadily. Keep the test tube 
slightly inclined. 

(d) Boiling Point by the Vapor Pressure Method. — 
Bend a <:la-< tube into a J shape, the arms being about 10 and 
20 cm. long. Fill the tube with mercury to 5 cm. above the 
bend. Place a lew drops of alcohol or ether in the short arm, 
tilt it till the mercury reaches nearly to the upper end of short 
arm, and cautiously seal off the Bhorl end with a blow pipe. 
fit should be nearly dosed off before putting in the liquids. 
The tubes had better be filled beforehand by the teacher unless 

the students have been previously taught how to do it.) Place 
this tube in a vessel of water, heal and stir the water till the 
mercury take< the same level in both branch.--, then read the 
thermometer. When it does bo, how does the vapor pressure 



104 LABORATORY EXERCISES IN PHYSICS 

compare with the surrounding (atmospheric) pressure? Record 
the observed temperature, which is the boiling point of the 
substance. 

(e) Effect of Dissolved Salts on boiling point. Place 
a thermometer in the boiler and take the temperature of the 
steam while the water is boiling. Then open the top and 
throw in a teaspoonful of salt. Does the boiling stop? Repeat 
the observation of the steam temperature, increasing the heat 
if necessary. Does the addition of a substance in solution 
raise the boiling point? 

(/) Effect of Surface of Containing Vessel. — Boil water 
in a glass beaker, previously cleaned with acid and then with 
soap suds and distilled water. Boil distilled water in the 
beaker and take its temperature. Let the water cool a little 
and then drop in a few chips of copper or brass, renew the heat- 
ing and again take the temperature. Does the boiling point 
depend on the nature of the surface of the vessel in which it is 
boiled? 

(g) Effect of Pressure on the Melting Point of Ice. — 
Slowly squeeze a rectangular piece of ice in a vise or a letter 
press. Does melting go on much more rapidly than it did 
before? Does the work done in squeezing the ice help the 
heat energy to melt it? What facts can you cite to prove that 
ice expands when it freezes and contracts when it melts? 
Can you explain why substances that contract when they melt 
have their melting points lowered by pressure? 

Exercise Number 29 

DEW POINT AND RELATIVE HUMIDITY 





References 




A 239 


GP 255-256 


J 59-67 


C & C 341 


H276 


M & T 132-134 


GE 157 


H & W 190-192 


W & H 126-130 



The Purpose is to find the temperature at which 
the water vapor will condense from the atmosphere 
of the laboratory (i.e. the dew-point), and to calcu- 



HEAT 105 

late the relative humidity (i.e. how near the moisture 
in the room space is to the pressure of saturation). 

The Apparatus is very simple, consisting merely 
of a brightly polished nickel-plated cup, a thermom- 
eter, some water and some snow or chips of ice. 

Operations. — (a) Partly fill the cup with water, 
which should be at or slightly above the temperature 
of the room. See that the outside of the cup is 
bright and perfectly free from all spots or tarnish. 
(Breathe on it, and polish with flannel or chamois 
skin if necessary.) Add snow or chips of ice, a very 
little at a time, with constant stirring, watching at- 
tentively for the first formation of dew on the bright 
outside surface of the cup below the water line. It 
will be recognized by a dimness in contrast with the 
polished surface where the dew has not yet begun 
to form. Take the temperature when the dew first 
begins to appear. Be careful not to breathe on the 
cup. Why? 

In winter the dew point is likely to be below 0° C. In case 
the dew does not appear on the cup when its temperature has 
reached 0° pour off the water and stir in salt with the ice. 

(1)) Having cooled the cup a little below the tem- 
perature of the dew point, wipe off the dew and begin 
to add warm water, a very little at a time, stirring con- 
stantly until the thin coating of dew which will have 
formed on the outside has just disappeared; then 
take the temperature. Theoretically this should be 
the same as that at which dew began to deposit, but 
practically the first temperature will probably be a 
little lower than the dew point, and the second a 



106 LABORATORY EXERCISES IN PHYSICS 

little higher. Hence the mean of the two readings 
will be nearer the true value than either of them. 

(c) Having observed and recorded the dew point, 
read and record the temperature of the air, turn to 
the table, Pressures of Saturated Water Vapor (Ap- 
pendix G) and take from it the pressure of saturated 
water vapor corresponding to the temperature of the 
air when your experiment was made. Take also the 
vapor pressure corresponding to the temperature that 
was the dew point at the same time. Find what 
percent the latter is of the former. This ratio or 
percentage is the Relative humidity, i.e. it is the 
ratio of the pressure of the vapor in the room to the 
pressure which would he exerted by the vapor if in 
sufficient quantity to saturate the room at the observed 
temperature, and it tells how nearly saturated the 
room space is. 

Lessons. — Answer in complete sentences: (a) Do 
you and your classmates exhale water vapor? If 
you do not know, breathe on any cold bright surface 
and look at it for evidence. Also remember the 
cloud which issues from your mouth or nostrils on a 
very cold day. Should you find the relative humid- 
ity of the school room higher after it has been occu- 
pied for some time, than before ? Compare relative 
humidities determined in the room at different times 
during the laboratory period or day. 

(b) With a given amount of moisture in the room 
will the relative humidity be higher or lower as the 
temperature is raised? Why does artificially heated 
air feel so dry? What is the remedy? 



HEAT 107 

(c) Will the dew point of a room be raised or 
lowered by boiling water in it ? What effect will 
this have on the relative humidity ? 

(d) Other things remaining the same, what effect 
does cooling the air have on its relative humidity? 
What happens when the out-door air is cooled till its 
relative humidity is 100 per cent, — first, when the 
temperature is above 0° C. (or 32° Fah.); second, 
when it is already below 0°CJ 

(e) What difference in conditions determines 
whether water vapor in the air shall be deposited as 
dew or as frost? 

OPTIONAL PROBLEMS 
(a) Determine the dew point and relative humidity in 
your home with a silver or tin cup or even an ordinary drink- 
ing glass and an ordinary thermometer. (If the thermometer 
has a tin case you can slide it out of the case. You will have 
to convert each Fahrenheit reading to Centigrade in order 
to use the vapor pressure table. To do this, subtract 32° 
and multiply by B / 9 .) Compare the result with the relative 
humidity taken out of doors. If there is a difference, ac- 
count for it. Phj^sicians state that the relative humidity for 
best indoor conditions should be kept as high as 50 per cent. If 
you find that of your home lower, examine your furnace (if 
the house is thus heated) and sec if there is a pan in the hot 
air jacket designed to hold water to be evaporated into the 
air that is conveyed into the rooms. If there is such a pan 
see to it that it is kept filled. If there is no such provision have 
water exposed in open vessels near the registers, radiator-, or 
grat< 

(6) Make a determination of the dew point and relative 
humidity out of doors and compare it with that made by the 
weather observer at the same time. (If you live in a city 

where a weather station IS located and it is not published in 
the daily papers you can get it from the observer by tele- 
phone.) 



108 LABOBATORY EXERCISES IN PHYSICS 

Exercise Number 30 
specific heat 

References 

A 225-226, 309-311, 242, 217 H 281-283, 253, 254, 258, 262 

C 246-248, 224-226, 229-232 H & W 205-210, 197-199, 202 

C & C 325-328, 343-347, 350, 351 M & T 125, 126, 138-140, 
GE 130-135, 158, 159, 163 147-152 

GP 219-224, 257, 382 W & H 107-109, 121-123, 125 

Purpose. — In this experiment the specific heat of a 
metal is to be determined b} r the method of mixtures. 

Apparatus. — This consists of the following: — 

(a) Balance, weights, and pincers. 

(5) The boiler of Exercise 28, with the cup which 
fits into the boiler in place of the cover. 

(e) A Bunsen burner. 

(c?) A calorimeter, consisting of a cup of thin brass, 
nickel plated, supported upon a cork in a jar or box, 
and packed around with cotton-batting or felt. 

(e) Perforated wooden covers for the cup and 
calorimeter. 

(/) Two thermometers. 

Materials. — The substance whose specific heat is 
to be determined, may be in the form of punchings 
or short clippings of wire or a loose roll of the sheet 
metal. A supply of cold water should also be at 
hand. 

Operations. — (a) Half fill the boiler with water 
and place the Bunsen flame under it. 

(5) See that the metal has been thoroughly dried, 
either on top of a radiator, or in a drying oven, and 



HEAT 109 

weigh it to .1 g. If the metal is in loose form, it 
may be weighed in the calorimeter. 

(<?) Transfer the metal to the cup, insert the latter 
in the boiler, put on the cover, and cautiously thrust 
the thermometer through the perforation into the 
midst of the metal. 

(c?) Weigh the calorimeter ; place in it the amount 
of water specified by the instructor ; and, having 
dried the outside, weigh it to .1 g. Place a ther- 
mometer in the water, stirring it occasionally. 

(e) When the temperature of the metal has become 
stationary, see that everything is in readiness for 
quickly transferring the heated metal to the calori- 
meter. It is best to have the boiler at the right 
hand, the calorimeter at the left. 

(/) Now read the temperature of the water and the 
metal to .1°, as nearly as possible at the same moment. 

(#) Immediately after these temperatures are taken 
remove the thermometers, slightly tilt the calorim- 
eter toward the cup with the left hand, carry the 
cup, with the right band, toward the calorimeter, 
and empty the metal into it, by quickly inverting 
the cup over the calorimeter. Instantly cover the 
calorimeter ; insert its thermometer through the 
perforated cover; and cautiously stir the metal and 
water together by means of the thermometer, watch- 
ing the mercury column attentively. 

(h) When the temperature has reached its highest 
point, if ascending, or its lowest if descending, record 
its reading to .1° as the temperature of the mixture. 

(i) Dry the calorimeter and return the metal. 



110 LABORATOBY EXEBCISES IN PHYSICS 

Remarks. Calculations. — (a) Great care should be taken 
not to spill any of the metal or water after it has been weighed. 
(Why?) 

(b) In this exercise two students may work together, divid- 
ing operations so as to save time, especially at critical moments. 
Thus the first may read the temperature of the metal and 
transfer it to the calorimeter, the second taking the tempera- 
ture of the water, and so on throughout. The division of labor 
should be planned before beginning the experiment. 

(c) The mass of the water is obtained by subtracting that 
of the calorimeter from that of the calorimeter and water ; and 
that of the metal is obtained in a similar manner. 

(d) The relative amounts of metal and water should be so 
chosen as to have the mixture come as nearly as possible to the 
temperature of the room. Thus the errors due to radiation 
and conduction will be nearly eliminated. (Why?) 

To secure the best results, the water should be ten de- 
grees or more below the temperature of the room ; and the 
relative masses, so chosen that the mass of the water multi- 
plied by the difference between its temperature and that of the 
room equals the mass of the metal multiplied by the difference 
between its temperature and that of the room, multiplied by 
its specific heat. The teacher may well make a preliminary 
experiment and calculation, and roughly indicate the amounts 
of metal and water. The actual amounts will necessarily 
depend on the size of the calorimeter and the kind of metal 
used. For a calorimeter of about 350 cc. capacity, 300 g. 
of copper and 100 g. of water are approximately the right 
proportions. 

(e) If the water is not cool enough to give a suitable tem- 
perature range (at least 10°), it should be kept cool by a bit of 
ice. No unmelted ice should remain in the calorimeter, however, at 
the time of mixing. 

(f) If but one thermometer is available, the temperature of 
the metal must be taken when it has become stationary, and 
the thermometer transferred to the water in order to get the 
temperature of the water and calorimeter. 



HEAT 



111 



Data. — Tabulate the quantities as indicated below 



Name of metal 




Temperature of metal 


tm °C 


Temperature of mixture 


t 




Temperature range of metal 


tm — t 




Mass of metal aud calo- 
rimeter 




cr 


Mass of calorimeter 


J/c 




Mass of metal 


Mm 




Amount of heat given out 
by metal 


S m XM m X {tm — t) 


calories 


Temperature of mixture 


t 


°C 


Temperature of water 


tiv 




Temperature range of water 


t — tm 




Mass of water and calo- 
rimeter 




g 


Mass of calorimeter 






Mass of water 


M w 




Amount of heat absorbed by 
water 


1 x Mm x (t — t u ) 


calories 


Temperature of mixture 


t 


°C 


Temperature of calorimeter 


tc(=t w ) 




Temperature range of calo- 
rimeter 


t t, 




Mass of calorimeter 


Me 


g 


Amount of heal absorbed by 

calorimeter 


|X .09xM c X(t—tc) 


calories 


Specific heat of the metal 


Sm = 





112 LABORATORY EXERCISES IN PHYSICS 

Heat Equation. — Equate the total amount of heat 
given out by the metal with the total amount ab- 
sorbed by the water and calorimeter. (Why?) 

S m is the only unknown quantity. Solve the 
equation and find it. 

Sources of Error. — (a) Those involved in the 
temperature readings are most important, an error 
of .1° in a range of 10° amounting to lfo. Hence the 
temperature range of the water should be made as 
large as practicable. (How?) 

(5) Errors also occur in mass determination, and 
from losses or gains of heat by radiation and con- 
duction. 

(<?) Since the calorimeter does not wholly come 
into contact with the mixture, only part of it is sub- 
ject to the entire temperature range. If less than 
half filled it is fair to assume that half its mass 
changes temperature ; and the error involved in this 
assumption is small, because its thermal capacity is 
relatively small. If a larger portion is filled, a cor- 
respondingly larger fraction should be assumed. 

(d) Any loss of time in mixing, after reading the 
temperatures, and any loss of metal or water by 
spilling causes errors. (Why?) 

Lessons. — Practice is given in the determination 
of an important physical constant, and in the use of 
the requisite apparatus, and in handling the equa- 
tions pertaining to the transference of heat units 
when temperature changes take place. 

Applications. — Try to explain the enormous effects 
of the large specific heat of water on climate. 



HEAT l^J 

Exercise Number 31 
latent heat of fusion 

References 

A 244, 245 a GE 145-148 J 43 

C 249 GP 239, 243 M & T 135-137, 138- 

C & C 329-333 H 284 140, 147-152 

H & W 211, 219, 220 W & H 112, 114 

Purpose. — The latent heat of fusion of ice is to be 
determined. 

Apparatus. — The boiler, calorimeter, scales, 
weights, pincers, and two thermometers are needed. 

Materials. — The materials used are cracked ice, or 
snow, and water. 

Operations. — (a) Place a thermometer in the calo- 
rimeter, and, after a while, note its temperature. 

(J) Thoroughly cleanse the boiler, if necessary ; 
half fill it with water and heat it. 

(V) Weigh the calorimeter. 

(d) When the water is nearly at the boiling point, 
pour into a beaker as much as will fill about two- 
thirds of the calorimeter, and determine the mass of 
the beaker and water. 

(e) Meantime, have ready on a cloth or blotting- 
paper, in the coolest place available, about as much 
cracked ice as. when melted, will fill one-third of the 
calorimeter. It is to be kept as dry as possible till 
used. 

(f) When the water has cooled to about 70° C, 
take its temperature to the tenth of a degree, and 



114 LABORATORY EXERCISES IN PHYSICS 

immediately pour into the calorimeter the ice, and 
then as much of the warm water as will nearly fill it. 
Instantly, put on the perforated cover, insert a ther- 
mometer, and with it keep stirring the mixture until 
the ice is melted. Stir gently, so as not to break the 
thermometer. 

Cff) Watch the mercury, which will become sta- 
tionary for a moment just as the ice disappears ; at 
this moment read and record the temperature of the 
mixture. 

(A) Weigh the calorimeter and its contents ; also 
weigh the beaker with any water that may have 
remained in it. 

Calculations. — To get the mass of the water used, 
subtract the mass of the beaker and water remaining 
in it from the mass of the beaker and water before 
pouring. 

To get the mass of the ice, add the mass of the 
water to that of the calorimeter, and subtract this 
sum from the combined mass of the calorimeter and 
its total contents. 

The temperatures should be read as accurately as 
possible to the tenth of a degree. 

The weighings are more than sufficiently accurate 
if made to the tenth of a gram. (Why ?) 

Data. — Tabulate the observations as indicated 
on the following page. The factor .09 in the quan- 
tity of heat gained or lost by the calorimeter is the 
specific heat of the brass of which the calorimeter 
is made. 



HEAT 



115 



Temperature of water 


t w 


o 


Temperature of mixture 


t 


o 


Temp, range of water 


tw — t 


o 


Mass of beaker and water 




g- 


Mass of emptied beaker 




g- 


Mass of water 


M w 


g- 


Heat given out by water 


1 x M w x {t w — t) 


calories 


Temp, of calorimeter 


te 


o 


Temperature of mixture 


t 


o 


Temp, range of calorimeter 


(te—t 
I or 
\t — te 


o 


Mass of calorimeter 


Mc 


0". 


T , A ( ' ) by calorim- 
Heat j or \ J 

' gained ' 


/ .09 X M c X (t c — t) 

J 

I .09 X 3/c X (t - tc) 


calories 


Mass of calorimeter and 
total contents 




g. 


Mass of calorimeter and 
water 


Mc + M w 


g- 


Mass of ice 


Mi 


g- 


Heat absorbed by ice in 
melting 


Li x Mi 


calorics 


Heat absorbed by melted 
ice in warming to t° 


1 x Mi x (t — o) 


calorics 


Latent heat of ice 


Li (calorics per gram) 





116 LABORATORY EXERCISES IN PHYSICS 

Heat Equation. — Equate the total quantity of heat 
absorbed with the total quantity given out. (Why?) 
Solve for L^ the latent heat of ice, which is the only 
unknown quantity. 

If the calorimeter changes temperature, the quantity of heat 
lost or gained by it should be properly placed in the equation ; 
thus, if its temperature was higher than that of the mixture, the 
calorimeter lost heat, and the amount lost should be added to 
that lost by the ivater. 

Sources of Error. — (a) State the kinds of errors 
to which this experiment is liable in common with 
the preceding one. 

(6) What additional error may arise from wetness 
of the ice ? 

(/) If the ice or snow is collected from out doors 
when the atmospheric temperature is considerably 
below freezing, what source of error is present ? 
How may this further error be corrected or elimi- 
nated ? 

Lessons. — The exercise affords practice in the 
manipulations of heat measurement, and in the 
principles and methods employed in solving prob- 
lems pertaining to heat transferences when the latent 
heat of melting is involved. 

Applications. — Large quantities of heat must be trans- 
formed into molecular potential energy in order that ice 
may be melted. The reverse transformation occurs when- 
ever water freezes. Try to explain in detail the applications of 
these facts to refrigerators and ice-cream freezers, and to the 
prevention of sudden changes of temperature in the vicinity of 
lakes. Try also to think out how the first fact operates to 
reduce the severity of spring freshets in ice-bound streams. 



HEAT 



117 



Exercise Number 32 



LATENT HEAT OF VAPORIZATION 





References 


H & W 213. 218 


A 216 


GP 250 


J 54-55 


C 250 


GE 119-151 


M&T 135-137, 138 


C & C 335. 312 


H 285, 286 


140. 147-152 



Purpose. — It is proposed to determine the latent 
heat of vaporization of water. 

Apparatus. — (a) The boiler used in the last three 
exercises is to be furnished with a water-trap and 
delivery tube, 
as shown, and 
18 inches of 
rubber gas tub- 
ing for con- 
necting them 
with the boiler. 
All should be 
tightly fitted, 
so that steam 
can escape from 




Fig. 22. — Calorimeter, cover, and water-trap : 
Ij. delivery tube : T, water-trap : C, rubber tube 
leading from boiler. 



the boiler only through the end of the delivery tube. 

(b) A thick band of paper, or a wooden tube 
holder, is necessary for handling the hot apparatus. 

(e) Two thermometers, balance, weights, and pin- 
cers arc to be near at hand. 

Operations. — (a) Half fill the boiler with water, 
generate steam, and take its temperature as in Exer- 
cise 28. 



118 LABORATORY EXERCISES IN PHYSICS 

(5) Remove the thermometer, and lay it in a safe 
and convenient place. With the holder, remove the 
tall tubular cover from the boiler, and screw on the 
flat cap.* 

(tf) See that the trap and delivery tube are emptied 
of water, and connect them with the outlet tube of 
the boiler. 

(<#) Weigh the calorimeter, and having added 
about 200 cc. of water, weigh again. These weigh- 
ings should be made while waiting for the water to 
boil. 

(e) Take the temperature of the water, which 
should be at least 10° below that of the room. (If 
necessary, cool it with bits of ice before weighing. 
No ice, however, should remain unmelted at the time of 
recording the temperature.^) 

(/) Immediately after taking the temperature of 
the water, introduce the delivery pipe through the 
perforated cover, and allow steam to pass vigorously 
through the water. A thermometer (better pre- 
viously warmed in the hand to about 10° above the 
temperature of the room) should be inserted through 
a second hole in the cover. 

(#) Move the delivery tube about in the water, 
but do not place it so far below the surface that 
you cannot plainly hear the rattling of the collaps- 
ing steam bubbles. 

Qi) When the temperature of the mixture is as 
far above that of the room as the water temperature 

* If the conical topped form is used, the openings should be 
closed with stoppers. 



HEAT 119 

was below it, withdraw the delivery tube, and as soon 
as the temperature ceases to rise with continued 
stirring, record it. 

(7) Weigh the calorimeter with its contents, and 
from the three weights now recorded deduce the 
mass of the original water and also that of the con- 
densed steam. 

(j) If time permits, read the barometer and attached ther- 
mometer ; correct the barometer reading for temperature as in 
Exercise 28, and calculate the temperature of the steam by adding 
to 100° .037' for every millimeter by which the barometer col- 
umn stands above 760 mm., or subtracting .037° for every mil- 
limeter by which the barometer column stands below 760 mm. 
The boiling point thus calculated is likely to be more nearly 
correct than that taken by the thermometer. 

Data. — Enter all the observations as soon as they 
are taken, in a ruled tabular form like that on the 
next page. 

Heat Equation. — Equate the sum of the quan- 
tities of heat absorbed by the water and the calo- 
rimeter, with the sum of the quantities given 
out by the steam in condensing and by the re- 
sulting water in cooling to t° ; and solve for Z,, 
the latent heat of steam, which is the only unknown 
quantity. 

Sources of Error. — (a) State those pertaining to 
each kind of observation, and to radiation and con- 
duction. Explain how they arc provided against by 
the methods adopted, 

{h) Against what very important error does the 
water trap provide ? 



120 LABORATORY EXERCISES IN PHYSICS 
Numerical Data 



Temperature of the water 


t w 


°C. 


Temperature of the mixture 


t 


°C. 


Temperature range of water 


i i w 


°c. 


Mass of calorimeter and 
water 




g- 


Mass of calorimeter 




g- 


Mass of water 


M w 


g- 


Quantity of heat absorbed 
by water 


lxM w x (t-t w ) 


calories 


Quantity of heat absorbed 
by calorimeter 


.09xM c x(t-t w )x% 


calories 


Mass of calorimeter, water, 
and condensed steam 




g- 


Mass of calorimeter and 
water 




a*. 


Mass of condensed steam 


M, 


g- 


Quantity of heat yielded by 
steam while condensing 


L s x M 8 


calories 


Temperature of the steam, 
i.e. boiling point 


ts 


°C. 


Temperature range of con- 
densed steam 


t s -t 


°C. 


Quantity of heat yielded by 
condensed steam in cooling 


1 x (t a - t) x M s 


calories 


Latent heat of steam 


L, 


calories 
per gram 



HEAT 121 

Lessons. — These are similar to those derived from 
the two preceding exercises. The student should 
state them concisely. 

What fundamental principle of Physics is as- 
sumed in the heat equations of Exercises 30, 31 
and 32 I 

Practical Applications. — Try to think out the appli- 
cations of the high latent heat of vaporization of 
water and other liquids in the following cases: 
steam-heating apparatus, effect of evaporation and 
condensation in modifying atmospheric temperature, 
prevention of too rapid evaporation and condensa- 
tion of moisture in nature, severity of burns caused 
by steam, loss of energy in a non-condensing steam 
engine, porous water-coolers, cooling effect of bay 
rum, relief from excessive bodily heat by perspira- 
tion and fanning, ice-machines, solidification of lique- 
fied gases by their own evaporation, the production 
of extreme low temperatures by the evaporation of 
liquid air. 



CHAPTER IY 

MAGNETISM AND ELECTRICITY 

Exercise Number 33 
lines of magnetic force 

References 

A 365-369 GE 337-343 H & W 221-226 

C 256-268 GP 486-494 W & H 240-251 

C & C 358-377 H 291-301 JJ 68-87 

M & T 199-206, p. 242, Sug. 1 

Purpose. — The purpose of this exercise is to de- 
termine the positions and directions of the lines of 
force in the magnetic fields of bar-magnets. 

Apparatus. — This 
consists of two bar- 
magnets, a box of fine 
iron filings, a sifter, 
a small compass, a 
board with grooves as 
shown, and a square 
of window-glass or 
glazed paper of the same size as the board. The 
sifter is either a square of fine wire gauze with its 
edges bent up, or a little bag of muslin. 

122 




MAGNETISM AND ELECTRICITY 123 

Part A 

Operations and Observations. — (a) Place a magnet 
in one of the grooves and near the centre of the 
board. The flat surface of the magnet should not 
project above that of the board. Lay the glass or 
paper over the magnet and fasten it down with bits 
of soft wax or with thumb-tacks. 

(b) Determine the poles of the magnet. The 
north-seeking pole is that which repels the north- 
seeking pole of the compass-needle. (Why?) 

(e) Place some filings in the sifter, and by gently 
tapping it with a pencil sift the finest iron dust 
through it upon the glass (or paper), distributing 
them evenly, but not too thickly, all over the space 
around the magnet. 

(c?) Tap the board very lightly with the pencil or 
a ruler, using vertical blows only, and striking at 
different points successively until the filings have 
come into their positions of equilibrium in response 
to the resultant magnetic forces acting upon them in 
their respective parts of the field. 

(e) Now, upon the note-book page make a diagram 
of the magnet and the filings. The copy of the out- 
lines of the magnet, and of the curves into which 
the filings have settled in all parts of the field, 
should be as faithful as you can make it. If not of 
the same size, the proportions should be carefully 
preserved. Letter the poles iVand S. 

(/) Place the compass, successively, near each 
corner of the magnet, and also opposite the middle 



124 LABORATORY EXERCISES IN PHYSICS 

of each end and of each side ; at each of these points 
observe the position into which the needle settles ; 
and at the corresponding position on the diagram 
draw a short arrow with its point in the position of 
the north-seeking pole of the needle. 

(^) Remembering that the lines represented by the 
filings are not broken, but continuous, draw several of 
these full lines on each side of the axis of the mag- 
net. Note that they are closed curves (but not circles 
or ellipses), each one passing out of the north-seek- 
ing pole of the magnet and around on the outside 
toward the south-seeking pole, then through the 
body of the magnet to the point where you began to 
trace it. Note also that the curves are bisymmetri- 
cal with respect to the axis of the magnet. 

(Ji) Over the diagram write the heading, Field of 
a Single Bar Magnet ; and under it write, " Each 
line of force represents at any point the direction 
which a free north-seeking pole would take at that 
point in consequence of the resultant magnetic force." 



Part B 
(a) Arrange the magnets as 





J3_ 




s. 






Fig. 24. 



shown in either 
diagram (Figure 
21), and repeat 
all the operations, 
again drawing ar- 
rows at the char- 
acteristic points 
of the field. 
(b) Above the 



MAGNETISM AND ELECTRICITY 125 

diagram write the heading, Field of Two Bar Mag- 
nets, Side by Side (or End to End), Like Poles 
Adjacent ; and below the diagram state what the 
lines represent, as before. 

Part C 

(a) Place the magnets as in one of the diagrams 
of Figure 21, — the one not chosen in Part B, — but 
reverse one of the magnets so that unlike poles shall 
be adjacent. 

(6) Make all observations and records as in the 
preceding cases. 

Inferences and Lessons. — (a) Is the magnetic field 
confined to the plane of the board, or does it include 
all planes ? How can this be proved ? 

(J) In each case, where is the strength of field the 
greatest ? 

(<?) Show by small diagrams the arrangement of 
the lines of force between two poles that are repelling 
each other and between two poles that are attracting 
each other, and label them appropriately. 

(c?) In investigating magnetic properties and 
their consequences it is very important to know 
definitely the directions of the lines of force and the 
relative strengths of different parts of the field. 

Additional Work. — If there is time (a) place a small rect- 
angle of soft sheet-iron between the two poles in the arrange- 
ments of Parts B ainl ('. and sketch the field, stating concisely 
what changes in the paths of the lines are due to the perme- 
ability of the soft iron. 



126 LABORATORY EXERCISES IN PHYSICS 

(b) Map the lines about a bar magnet pole in a plane per- 
pendicular to the axis of the magnet. 

(c) Map the field of a horseshoe magnet lying flat and also 
with poles up. 

(<7) Very pretty results may be obtained by mapping the 
field of three or more magnets arranged in a triangle, square, 
pentagon, cross, etc. 

Permanent Maps. — If the student does something in photog- 
raphy, he will find it very fascinating to repeat these experi- 
ments in a dark room, using a photographic plate instead of 
the glass or paper. Make the map by ruby light on a slow 
or medium i:>late, exposing to the light of a match at one or 
two feet distance, then developing and fixing in the ordinary 
way. Developing or printing-out papers also give excellent re- 
sults. In all cases carefully avoid over-exposure. 

Another method is to coat a sheet of ordinary glass with 
shellac varnish ; dry it ; make the map ; and then warm it on 
a sand-bath over a stove until the shellac softens and the filings 
sink into it. 

Maps made on glass, when backed with ground or opal 
glass and bound or framed for transparencies, will make pretty 
ornaments. 

Pieces of watchspring, straightened and magnetized, make 
excellent magnets for all these experiments, and cost nothing. 

Exercise Number 34 
field of electromagnetic force 

References 

A 375, 377, 381 GE 349-354, 308, 309 H & W 252 

C 269, 270, 291, 315, 317-319 GP 445, 507-514 JJ 119-126 

C & C 452-459 H 371-376 M & T 207- 

T 195-204, 389, 390, 393 W & H 278, 281-284 214,226-228 

Purpose. — It is proposed to investigate the 
magnetic field about a current-bearing conductor. 



MAGNETISM AND ELECTRICITY 127 

(a) When straight. (5) When in a single loop. 
(e) When in a helix. (rf) When in a flat coil 
(e) When the helix or coil is associated with a soft 
iron core. 

Apparatus. — The apparatus and its arrangement 
are shown in the diagram. A drawing made from 
the objects themselves should be placed in the note- 




Fig. 25. — Conductors arranged so that their fields of electromagnetic 
force can be mapped. 

book. Iron filings, sifter, and compass are provided 
as in Exercise 33; also a square and a rectangle of 
soft sheet-iron. 

Operations and Observations. — (a) Dip the bare 
wire, A. into the box of filings, and make a sketch of 
what you see. 

(J) Sift filings over the two boards, tap the boards 
till the filings find their places, disconnect the cur- 
rent and sketch the fields about B, C, and D. If 
you are using the dynamo current in s< ries with other 
tables, do not disconnect. The teacher will attend to 
that . 

(<?) Place tlic compass in the characteristic parts 
of each held, B, C, 2), and draw thin arrows in cor- 
responding positions in your diagrams just as in 
Exercise 33. 



128 LABORATORY EXERCISES IN PHYSICS 

(d) Place the rectangular strip of sheet iron 
lengthwise in the helix, (7, but not touching it, and 
similarly place the square in the flat circular coil, D, 
repeat operations (5) and (<?), making new diagrams, 
or stating each effect in words, as preferred. 

(e) The direction of the current will be given you 
by the teacher. Indicate it by short, thick arrows in 
all parts of the circuit and especially near the coils. 

(/) Do not crowd the diagrams, nor make them 
too small. It is better to put only one drawing on a 
page. Label the fields, Straight Wire, Helix, etc. 

Inferences and Lessons. — Make clear, concise sen- 
tences answering the questions below. 

(a) What is the form of a line of force about A or B ? 

(5) Looking along the wire in each case with the 
direction of the current, do the lines of force go 
clockwise or counter-clockwise ? 

(V) What is the direction of the lines of force if 
the current is coming toward you ? 

(<#) Is the field of what it should be if the lines 
of force are the resultants of the lines of force of 
several loops like the single one B ? 

(e) Compare the fields of C and D with those 
which would belong to similarly shaped bar magnets. 

(f) How is the strength of the field affected by 
increasing the strength of the current ? By increas- 
ing the number of turns in the coil ? What effect 
is due to the permeability of the soft iron core? 

(g) What name is given to a helix or flat coil hav- 
ing a soft iron core and carrying a current? What 
special advantages has it ? 



MAGNETISM AND ELECTRICITY 129 

(Ji) What can you infer as to the behavior of all 
such coils and helixes toward each other and toward 
magnets ? Try to find applications of electromagnets. 

Note. — The current strength should be from five to twenty- 
Amperes in order to get satisfactory curves, and is best fur- T 
nished by a direct current dynamo or storage battery, all the 
apparatus in the laboratory being joined up in series. In this 
case the teacher will regulate the current by means of a suita- 
ble resistance, and inspect the connections before turning on 
the current. If the school is not equipped with a dynamo one 
or two chromic acid cells are to be connected in series with each 
apparatus. 

Exercise Number 35 
short distance telegraphy 

References 

A 432-434 GE 379, 380 J J 290-298 

C 316 GP 550, 551 M & T 209-215 

C & C 507-510, 512, H 419-421, 424, 427 T 499, 500 

513 H & W 252 W & H 286 

Purpose. — The purpose of this exercise is to set 
up a short distance telegraph line of two stations, to 
diagram the arrangement, to trace the current 
through the circuit, to operate the instruments, and 
to explain their action. 

Apparatus. — (a) Call the two stations A and B. 
At each station there should be one gravity cell, one 
key, one sounder, sonic pieces of wire, and a couple of 
double connectors. 

(J>) A single wire representing the line wire is 
supported on insulators and runs from A to B. 



130 LABORATORY EXERCISES IN PHYSICS 



ADJUSTING SCREWS) 
CONTACT^ 



Operations, — (a) At one station, e.g. A, connect 
the — electrode of the battery cell to a wire leading 

from a gas pipe or 
water pipe. Both 
wire and pipe 
should have been 
filed till bright, and 
the wire tightly 
wound a half-dozen 
times round the 
pipe, or still better, 




Fig. 26.— Morse Key. 



ADJUSTING SCREWS- 



soldered to the pipe, thus securing a good " ground 
connection." 

(6) At the other station make a similar ground 
connection with the + electrode of the battery 
cell. 

(c) At each station, connect the free electrode of 
the battery with 
one terminal of 
the key. Here 
and throughout, 
use double con- 
nectors where 
there are no bind- 
ing-posts. 

(d) Draw a 
neat and legible 

,. c ii Fig. 27.— Telegraph Sounder. 

diagram of the 

cell and connections as far as now made. 

(e) At each station connect the free terminal of 
the key with one of the binding-posts of the sounder. 




ELECTRO MAGNET 
SPRING 
.BINDING POSTS 



MAGNETISM AND ELECTRICITY 131 

(/) Join the other binding-post of the sounder 
to the line wire. The " circuit " is now complete or 
" closed '' and the apparatus is " in series." 

(</) Before attempting to operate, see that both 
keys are closed by means of their side levers, or 
" switches," which are provided in order that the 
keys may always be closed when no message is 
being sent. (Why ?) Now complete the diagram of 
the circuit, including all the apparatus at both stations 
and the line wire, and having due regard to the pro- 
portions of the different parts of the apparatus. 

(K) By means of arrows, trace the path of the cur- 
rent from the zinc of your cell — through the fluid, 
then through the entire wire circuit, instruments, 
line, and ground — back to the zinc. 

(i) Now operate the circuit, sending from each 
station in turn such Morse signals as may be indi- 
cated by the teacher. 

(j) Make a separate sketch or diagram of the key 
and of the sounder. By reference to the parts as 
indicated by appropriate lettering briefly explain the 
action of each. Draw from the objects, not the cats. 

Precautions. — Since oxidized, greasy, or loose 
connections greatly diminish the current strength 
(Why?), see that all connections are scraped bright 
and clean and that the binding screws are firmly set. 

Lesson. — This exercise is designed to make the 
student acquainted with the proper method of set- 
ting up the instruments of a telegraph line, and with 
the manner in which the electric current is used in 
sending and receiving signals with them. 



132 LABOBATOBY EXEBCISES IN PHYSICS 



Exercise Number 36 

long distance telegraphy 

References 



A 432-434 

C316 

C & C 511-514 



GE 379-381 
GP 550-552 
H 423-425 
JJ 290-299 



M&T215-217 
T 499-501 
W & H 286 



ARMATURE CONTACT 
POINTS 



ELECTRO MAGNET 



Purpose. — The purpose of this experiment is to 
study the construction and action of the relay, and 
to learn why it is necessary on a line of high resist- 
ance. 

Apparatus. — (a) In addition to the apparatus of 
Exercise 35 a relay and two more cells of battery 

are needed at each 
station. 

(5) The same 
line wire may be 
used, but is sup- 
posed to be many 
miles longer, so 
that the additional 
resistance makes 
the current too 
weak to operate the sounder. If the teacher desire, 
he may insert a suitable resistance to represent that 
of the additional line wire. 

Operations. — (a) Examine the relay, and deter- 
mine which pair of binding-posts is connected with 
the ends of the magnet wire. These are called the 
main line posts. 




Fig. 28. — Telegraph Relay. 



MAGNETISM AND ELECTRICITY 133 

(5) The other two are called the local circuit posts. 
Trace the metallic paths from them to the air gap 
between the platinum contact point on the lever and 
that on the screw against which the lever strikes 
when the armature is attracted toward the magnet. 
Notice, when the armature is released and the lever 
flies back in obedience to the tension of its spring, 
that the screw against which it now strikes is in- 
sulated from it by a tip of hard rubber. Thus there 
is a break in the metallic path between the two local 
posts when the armature is not attracted; but this 
air gap is closed whenever the armature is drawn 
fonvard. 

(<?) If a battery cell and a sounder be placed in 
series with the two local posts, can the relay lever be 
operated by the hand, so as to act as a key, and thus 
to work the sounder? Why? Try it, and state 
what occurs. 

(d) Now (at each table) disconnect the local wires 
from their posts, join two cells in series, "ground" 
the —electrode of this "main line battery" at sta- 
tion A, and also ground the + electrode of the main 
line battery at station B. At each station connect 
the other electrode of the main line battery to one 
post of the key ; connect the other post of the key 
with one of the main line posts of the relay ; and 
join the free main line post of the relay to the line 
wire. 

(e) Diagram the arrangement, and, by means of 
thin arrows, trace the main line current throughout 
the circuit. 



134 LABORATORY EXERCISES IN PHYSICS 

(/) Send a signal from each station to the other 
in turn. If you fail to receive the signal, first see 
that the circuit is unbroken excepting at the sending 
key, and then, if you still fail, ask the instructor to 
assist you in adjusting the relay. 

(#) Connect the local battery and sounder in series 
with the local posts of the relay, as you did in opera- 
tion (<?). Can you now operate the relay at B by 
opening and closing the key at A (the key at B re- 
maining closed) ? Does the relay at A receive sig- 
nals sent from B in like manner ? Do the relays at 
A and i?, when thus operated, open and close their 
respective local circuits so that the sounders click in 
unison with them ? 

(Ji) Add the local circuits to your diagram, tracing 
the local battery currents through them. Use thick 
arrows to indicate that these currents are not the 
same as that on the main circuit, and are stronger. 

Lessons. — (a) Does the relay in operation (/) 
act just as the sounder did in Exercise 35? Does it 
make noise enough to be heard easily, or is the noise 
faint compared with that made by the sounder in 
Exercise 35 ? If the main line resistance be great, 
can the current work the sounder when connected as 
in Exercise 35 ? Why ? Is it, nevertheless, strong 
enough to operate the relay ? Does the relay lever 
act like a key to the local circuit ? How does it 
differ from a key with regard to the immediate source 
of the energy that moves it ? Does the sounder now 
make noise enough to be heard easily ? Is it the main 
battery current, or the sound, which is reenforced by 



MAGNETISM AXD ELECTRICITY 135 

the use of the local battery and sounder? State 
whether or not any of the local current gets into the 
main circuit, or any of the main line current into the 
local circuits. 

(b) From the object, make a careful drawing of the B 
relay, and briefly explain its action. Do not repeat f 
any statements made in answer to questions above. 

Exercise Number 37 

ELECTRIC BELLS AND DOMESTIC WIRING - 

References 

A 427, 428 C & C 515 H 418 

M & T 218 W & H 285 

The Purpose of the exercise is to learn how wiring 
is done for domestic electric bell service. 

The Apparatus, Fig. 29, consists of a wooden 
frame with partitions, which is to represent a sec- 
tional model of a house. Electric bells, push but- 
tons, battery cells, and annunciator indicators are 
mounted on the frame as shown in the diagram. A 
supply of insulated wires of various lengths are to 
be used for making the connections, and several 
binding posts, JB p v B p 2 , B p % , etc. serve to join 
the wires where in actual practice they would be 
permanently joined and covered with insulating 
tape. 

Operations. — | a | Remove the covers from a bell 
and a push button, and make a clear diagram of 
each. By reference to these diagrams, explain the 



136 LABORATORY EXERCISES IN PHYSICS 



action. The diagrams should be lettered, and the 
paths of the current clearly shown by arrows. 

(b) Beginning with the carbon of battery cell 
B a v connect it in series with B a 2 (i.e. carbon 
with zinc). From the carbon of B a 2 carry a white 
leading out wire to one binding post of the bell. 




Fig. 29. 

(c) With white wires, connect the other post of 
the bell through the indicator I with one side of the 
Front Door Fush Button P v Also connect the 
other side of I\ by the long, red return wire with 
the zinc of B a ± . 

(d) Diagram the arrangement, tracing out the 
circuit with arrows; then press the button to see if 
the current rings the bell and turns the indicator l v 

(e) In like manner, connect, diagram, and trace 
the circuits for P 2 -I 2 , P z -I z and P 4 -/ 4 . Test 



MAGNETISM AND ELECTRICITY 137 

them. | Use white wires from battery to button, 
red wires from button back to battery. 

(y | Connect, diagram, and test the circuits for 
the bells B and 2? with their push buttons jP 5 
and P. 

o 

OPTIONAL PROBLEMS 

(a) Connect the spark coil Sp with the battery and the 
lighter Gl as indicated. Diagram the circuit. Connect 
the gas burner with the gas supply by means of a rubber tube, 
and turn on the gas at the supply pipe. Operate and study 
out the action of the spark coil and gas lighter. (The reason 
why the coil gives a spark will be learned in Exercise 38 

(6) Connect the three bells in scries, i.e. so that the current 

from the battery through one bell after another, and back 

through a button to the battery. Diagram, trace circuit and test. 

(c) Connect the three bells in a parallel arrangement or 
multiple arc, i.e.. so that the current splits up among them. 

r uniting the branch circuits (shunts) at a common point, 
connect this point through one of the push buttons to the return 
wire. Diagram, trace currents with arrows, and see if all the 
bells will ring when the button is pressed. 

(d) A battery of four cells may be connected all in series, 
(i.e., carbon of 1 to zinc of 2. carbon of 2 to zinc of 3. etc.) 
or all parallel [i. e. all the carbons to the leading out wire. 
and all the zincs to the return wire), or in two series of two 
each, the two series being themselves joined parallel. Try 
to think out which of these arrangements would be best for 
the arrangement of the bells in od which best for the 

a in multiple arc. Confirm or overthrow your conclusion 
matter out and seeinsr which arrangement of the 

_ ment of the bells 
[Problems (b) and (c)]. 

(e) Introduce into the branch with one of the bells [as in 
Problem thus ma. 

•nt on that branch encounter much mor nice. 

: now ring well? [n g n ral, if a number of bells 

or other : worked in parallel by the 



138 LABORATORY EXERCISES IN PHYSICS 

same battery, how should the amounts of resistance that the 
branch currents have to overcome compare with one another? 
This problem suggests a very common trouble with bells and 
clocks when wired in multiple arc. 

(/) Bells at Home. — After Working out this Exercise the 
student should keep the bells at home in working order. The 
bell is adjusted by the little contact screw near the clapper. 
Printed directions for renewing the batteries are pasted on the 
jars. 



Exercise Number 38 

induced currents 

References 

M & T 229-237, 
A 388, 389 GP 515-521 268, 269 

C 229-305 H 396-398 T 222-226 

C & C 480-484 H & W 259-263 W & H 313-315, 

GE 356, 357 JJ 132-138, 140-142 327-329 

Purpose. — It is proposed in this exercise to in- 
vestigate the laws of induced currents. 

Apparatus. — The appliances consist of a coil of 
many turns of fine wire (secondary), and another of 
fewer turns of coarser wire (primary), which fits into 
the former ; a soft iron core, a bar magnet, a sensi- 
tive galvanometer (D'Arsonval or astatic), and two 
cells in series. 

Operations. — (a) Set up the galvanometer and 
connect its terminals by means of a shunt ; touch the 
galvanometer terminals to the leading wires from the 
battery, and make note of the direction of the current 
which gives a deflection to the right, so that in the 
experiments the directions of the induced currents 



MAGNETISM AND ELECTRICITY 139 

may be observed by noting the directions of the 
resulting deflection. Remove the shunt. 

(6) Connect the galvanometer terminals by long 
wires with the terminals of the secondary coil, keeping 
the coil and galvanometer as far apart as practicable. 

(<?) Thrust the north-seeking pole of the magnet 
into the secondary, note the deflection, and trace the 
direction of the induced current around the coil. 

(c?) From the direction of this current around the 
coil, determine the direction of its lines of force 
(Exercise 34), and state whether it caused the end 
of the coil into which it was thrust to be a north- 
seeking or south-seeking pole. 

Remember that if the current circulates counter-clockwise 
around the coil as you face its end, the lines of force come out 
of it ; and this end is a north-seeking pole. 

(e) Was the force of the coil in such a direction 
as to oppose or to assist the motion of pushing the 
north-seeking pole up to the coil ? 

(/) Now withdraw the north-seeking magnet pole, 
and note deflection, direction of current, direction of 
lines of force, and effect on the motion, as before. 

(//) Repeat all the observations and notes, using 
the south-seeking pole of the magnet. 

(Jt) Connect the terminals of the primary coil witli 
the battery; determine one of its poles from the 
direction of the current around it, or by a compass 
needle (Exercises 33, 34); and then repeat all the 
experiments and notes made with one pole of the 
magnet. 

(i) Reverse the cm-rent through primary. Does 



140 LABORATORY EXERCISES IN PHYSICS 

its polarity change ? Repeat all the experiments and 
notes as with the other pole of the magnet. 

(y) Repeat all the experiments with the two coils, 
having previously placed the soft iron core inside the 
primary (6). State whether the quality or magnitude 
of the effects has changed, and how. 

(&) Place the primary inside the secondary, and 
then (1) close circuit ; (2) open circuit ; (3) reverse 
the battery wires and close circuit ; (-i) open the 
circuit. Note all the results and compare them, 
quality and quantity, with those obtained by insert- 
ing and withdrawing the coil while the circuit remains 
constantly closed. 

(?) Insert the primary into the secondary and the 
soft iron core into the primary. Now repeat all the 
experiments made in (&) and compare results. 

Inferences. — State the effect produced (a) by in- 
creasing the number of lines of force passing in a given 
direction through a closed coil, (5) by diminishing 
the number of lines passing in the given direction 
through the closed coil (all the movements that were 
made either increased or diminished them). (Why ?) 

(<?) State how the magnitude of the induced 
E.M.F. is affected by the rate of change of the 
number of lines, which was increased or diminished 
in the various cases either by changing more lines or 
by quickening the motion so as to change the same 
number in less time. 

(d) State Lenz's Law, and say whether or not all 
the observations show that this law is verified in 
your experiments. 



MAGNETISM AND ELECTRICITY* 141 

OPTIONAL PROBLEMS 

(a) Reversibility of the Dynamo and Motor. — Mount 
two toy motors, A and B, on a board; and belt their two pulleys 
together with a soft cotton cord, or a weak rubber band. 
Join the binding posts of A with the two poles of a battery, 
and those of B with the terminals of a galvanometer. Does 
B act as a dynamo, and generate a current? Now inter- 
change the battery and galvanometer. Does B act as a motor, 
and A as a dynamo? Describe the transformations and 
transferences of energy. 

(6) Dissect One of the Machines, keeping the parts in 
a box cover. Diagram the parts. Re-assemble it, and trace 
the current through all the connections. 

With the aid of Figs. 134 and 135, Mann and Twiss' Physics, 
find out whether it is shunt or series wound. Change it from 
shunt to series, or vice versa; and operate it as motor and as 
dynamo. 

Exercise Number 39 
electrical resistance 

References 

A 350-353, 414-416 JJ 95, 98, 99-101, 106, 107, 151, 
C 312, 324 152, 154, 160-168 

C & C 460-463, 471, 473, 475, H 377-380, 383-389 

479 H & W 256 

GP 455, 470-473, 479 M & T 248-256, 258-265, 267- 
GE 315, 324-328 269 

W & H 279-280, 290-294 

The Purpose is to learn how the electrical resist- 
ance of a conductor is measured. 

Apparatus. — In one of the most widely used 
methods of measuring resistance, the Wheatstone 
Bridge is the principal instrument. It is connected 
by wires with a battery 11 0, a sensitive galvanom- 



142 LABORATORY EXERCISES IN PHYSICS 



eter G, and a wire coil of known resistance r r (Cf . 
Figs. 30 and 31, also Appendix F.) 

Theory of the Wheatstone Bridge. — Let there be 
an arrangement of conductors forming a divided cir- 
cuit as represented 
in the diagram. 

Let a current 
from the battery 
divide at A into 
two branches, and 
reunite at D ; and 
let the point be 
so chosen with 
reference to B that 
no current passes 




Fig. 30.- 



- Explaining the theory of Wheat- 
stone's Bridge. 



through a galvanometer, 6r, in connection with these 
two points. Then B and are equipotential points. 
(Why ?) Also, — 

let F 1 and r x be the fall of potential and the resistance 
between A and J5, 
F 2 and r 2 be the fall of potential and the resistance 

between B and D, 
F s and r 3 be the fall of potential and the resistance 

between A and (7, 
F± and r 4 be the fall of potential and the resistance 
between and J). 
Then F 1 = F s (being the falls of potential from A to 

the equipotential points B and (7), 
and F 2 = F± (being the falls of potential from the 
equipotential points B and C to i>). 



MAGNETISM AXD ELECTRICITY 



143 



F F 

£1 = ±_3 

F F ' 



(Why?) 



But 



^2 >2 ^4 *4 



(The fall of potential along any part of a conduc- 
tor is proportional to the resistance of that part.) 

... h = 7 Ji. (Why?) 

Corollary. — Since the resistances of conductors 
of uniform material and sectional area are propor- 
tional to their lengths, it follows that if ACD be a 
wire of uniform material and thickness, the ratio of 

the lengths of the segments A O and CD (i.e. — 3 L may 
be substituted for the ratio of their resistances f -3 j anc { 



we shall have • 



h 



If three of the quantities in 



T 2 L l 

either of the above proportions are known (or can be 
measured), the fourth can be calculated. 

Application of the Theory. — The shaded rectangles, 
Fig. 31, represent thick copper or brass strips whose 




Fig. 31. 



144 LABORATORY EXERCISES IN PHYSICS 

resistances are negligible unless extreme accuracy is 
sought. The straight wire Z 3 Z 4 is just a meter 
(sometimes a half meter) long, and as nearly as 
may be of uniform cross section. It is made of an 
alloy (German silver or platinoid) which has a rela- 
tively high resistance not greatly affected by small 
changes of temperature. This wire is stretched 
over a meter rule, and is divided by the sliding con- 
tact C into two segments whose resistances will be 
called r B and r 4 . Examine Figs. 30 and 31, and 
note that the distribution of resistances in them is 
essentially the same, i.e. they differ only as to 
exact shape. Hence the general theory applies to 
Fig. 31; and (since the wire Z 3 Z 4 is uniform) the 
corollary also applies to it. 

Measuring Resistance with the Bridge. — (a) Close 
the gap above A with the wire whose resistance is 
to be determined, making tight connections with the 
binding posts. Call its resistance r x or x. In like 
manner, connect the known resistance r 2 across the 
gap above D. If a box of resistance coils is fur- 
nished for this purpose, join its binding posts with 
those of the bridge by means of short, thick wires. 
(Why?) Connect the battery B a, the galvanom- 
eter G, and a telegraph key or a push button, as 
shown in the diagram. Take care that all the 
metallic contacts are scraped clean and bright and 
the binding posts firmly set. (Why,?) 

(b) See that the galvanometer is properly leveled, 
and that the pointer stands at zero. (Cf. Appendix 
F.) Close the key, and slide the contact piece C 



SOUND 145 

along the meter rule, until a point is found such 
that when contact is made there the galvanometer 
pointer shows no disturbance. Do not stretch or 
scrape the wire. (Why i) 

Remarks. — "When beginning the experiment, have the 
galvanometer shunted, and remove the shunt when the de- 
flections become small. First make contact with C at dis- 
tances of 10 cm. along the wire, beginning at the left end, 
until the galvanometer reverses its deflection: then go back 
toward the left end, making contact at distances of 1 cm. 
When the galvanometer again reverses, and the point of no 
deflection is thus located within 1 cm., go toward the right 
again by steps of 1 mm. 

Avoid heating the wire in any way. (Why?) 

Leave the key open when the bridge is not in use. 

It is best to select such a known resistance that the point of 
no deflection comes near the middle of the wire. This may 
be easily done in a rough preliminary experiment. When 
this plan is adopted the errors due to non uniformity of the 
wire are much less serious. (Why?) 

(c) Test the adjustment by seeing if equal and 

opposite deflections are caused by making contact at 

equal short distances on the right and left of the 

point of no deflection. If necessary, readjust until 

the point that satisfies this condition is found. 

'A Read and record in millimeters the lengths 

Z 3 and L A of the segments into which ("divides the 

wire. 

(e) From the corollary to the general theory it is 

/' L 

plain that r x = - ' 3 . Substitute the values of the 

three known quantities and calculate the unknown 
resistance. 

(f) Now interchange the known and the un- 



146 LABORATORY EXERCISES IN PHYSICS 

known resistances, repeat the operations, solve the 
equation for the new value of the unknown resist- 
ance, and take as the probable true value the mean 
of the two determinations. 

OPTIONAL PROBLEMS 

(a) Ammeter and Voltmeter Method. — Connect an 
ammeter in series with a glow lamp, and also connect a volt- 
meter as a shunt across the terminals of the lamp. Pass the 
current through the lamp so as to light it up, take a series of 
readings of the meters, and find the mean reading of each 
meter. From Ohm's Law, Ohms resistance = Volts lost in 
the lamp -r- Current strength in amperes. Calculate thus the 
"hot resistance 11 of the lamp. Compare this with its cold resist- 
ance obtained with the Wheatstone Bridge. Does the resist- 
ance of carbon rise or fall with increase of temperature? 

Since Power in Watts = Volts X Amperes, you have the 
data for calculating in watts the rate at which the lamp uses 
energy. Calculate it. 

(b) Find the Hot and the Cold Resistance of an electric 
heater, such as is sold for flat irons, chafing dishes, etc., pro- 
ceeding as suggested in Problem (a). State what effect raising 
the temperature of the metallic wire of the heating coil has 
on its electrical resistance. Compare with carbon (Problem a). 

(c) Relation of Resistance to Length. — Measure off 
(say) 6 meters of Number 28 B&S gauge German silver wire, 
and determine its resistance with the bridge. Determine also 
the resistance of § and of J of its length. Express decimally 
the ratio of each resistance to the corresponding length, and 
tabulate all the results. Do you find that the ratio of resist- 
ance to corresponding length is a constant one? State the 
law of resistance which may be verified by such experiments. 
The quotient obtained by dividing the resistance by the length 
in cm. also represents the resistance of a centimeter of wire of 
the given material and sectional area. This being known how 
may the resistance of any number of cm. be calculated? 

(d) Resistance and Sectional Area. — As suggested 
in Problem (c) measure the resistances R and R' ', of 6m. each 
of 28 and 16 or 18 German silver wire. With a micrometer 



SOUND 1*7 

screw caliper (cf. Appendix B Art. 5), determine their diameters; 
and from the diameters calculate their sectional areas, a and a'. 
Find the products Ra and R'a' ; and see how near equal they 
are. If they are so nearly equal that you may regard the 
difference as experimental error, you may write Ra=R'a'. 

Prove that if this equation is true then ■=.= —. State the 

R f a 

law of resistance which this proportion expresses. 

(e) Resistance axd Material. — Measure the resistance 
of 6m. of 28 copper wire, compare it with that of the German 
silver wire of the same dimensions. Other things being equal, 
the resistance of a German silver wire is found to be how 
many times as great as that of a copper wire? State the law 
of which this is a particular case. 

(/) Resistivity. — Having measured the lengths, sectional 
areas and resistances of any or all the wires mentioned in 

Problems (c), (d), and (e), find the quantity -j- for each (i.e. 

multiply the resistance of 1 cm. by the area of cross section 
in square centimeters). This quantity for a given substance is 
called its resistivity or specific resistance. 

Exercise Number 40 
study of a simple voltaic cell 

References 

A 346-349, 385-385 d H 346-355 

C 294-297 H & W 243-246 

C & C 428-442 JJ 30-36, 40-44, 47-55 

GE 297-304, 308, 309 M & T 207-212, 272-281 

(,P 429-441, 467 W & II 269-271, 271-277 

Purpose. — The purpose of this exercise is to in- 
vestigate the action of a simple voltaic cell. 

Apparatus. — The apparatus and materials consist 
of a battery jar, nearly full of dilute sulphuric acid 
fl part acid to 20 parts water), two zinc plates, one 
of them amalgamated with mercury, a copper plate, 



148 LABORATORY EXERCISES IN PHYSICS 



a wooden cleat with two saw cuts in which to 

support the plates, a 
compass, and a double 
connector. 

Preliminary Direc- 
tions. — (a) Caution ! 
Throughout the experi- 
ment the jars and plates 
should be kept in a tray 
of sheet lead provided 
for the purpose. The 
acid is very destruc- 
tive, and under no cir- 
cumstances should it 
be allowed to drip on 
the table or clothing. 
Should such an acci- 
dent occur, quickly wash 
away the acid with a 
weak ammonia solution, 
followed by plenty of water. 

(5) Do not inhale the unpleasant fumes. 
(<?) Do not allow the amalgamated zinc to touch 
either of the other plates. 

(c?) In describing the apparatus, make a diagram 
showing (1) cell with plates and liquid in position, 
wires joined, and compass needle in the observed 
attitude; (2) plates, marked respectively Cu (cop- 
per) and Zn (zinc); (3) electrodes, marked respec- 
tively + electrode and — electrode ; (4) solution, 
marked sulphuric acid; (5) direction of current. 




Fig. 32. — Showing method of sup 
porting and connecting the plates. 



MAGNETISM AND ELECTRICITY 149 

(e) After each observation, remove the plates 
promptly (to a jar of water, which should stand 
ready in the tray). 

(/) Before beginning each operation, see that the 
liquid has cleared of bubbles previously formed. 

Operations. — (a) Place the copper strip in the acid. 
Is any chemical action indicated by gas bubbles rising 
from the plate ? 

(6) By means of the cleat, support the copper and 
the unamalgamated zinc side by side in the acid, not 
allowing either the plates or their wire terminals to 
touch each other. Is there now any chemical action ? 
If so, from which plate do the bubbles come ? Note, 
as well as you can, the rapidity of the action, so as to 
compare it with that in other cases. 

(e) By means of a double connector, join the wire 
that leads from the copper (i.e. the + electrode) to 
the wire that leads from the zinc (i.e. the —elec- 
trode). Do bubbles rise from either or both plates ? 
If from both, from which plate do the most bubbles 
come off ? Is the action more vigorous than in 
Case (i) ? 

(d) Pass the wire in a north-south direction over 
the compass needle. Is the needle deflected ? As 
you look along the wire, does the north- seeking pole 
move in the clockwise or counter-clockwise direction 
with regard to the wire? Then, remembering the 
relation of lines of force to current which you 
learned in the preceding exercise, state whether the 
current passes along the wire from copper to zinc, or 
in the reverse direction. 



150 LABOBATORY EXEBCISES IN PHYSICS 

(e) Replace the unamalgamated zinc by the amal- 
gamated, leaving the circuit open ; and compare the 
observations with those of Case (6). Record the 
* result. 

(/) Join the electrodes. Where do the bubbles 
originate now ? Compare the vigor of the action 
with that in Case (c). Record the result. 

(#) Pass the wire over the compass, as in Case (&). 
Is the direction of the current the same ? Is the 
strength of the current greater (indicated by a 
greater deflection) ? 

(A) Compare the two zincs, and (if possible) note 
which has wasted the most by the chemical action. 
(The only certain way is to expose them equally and 
weigh each before and after.) Does the copper show 
any signs of wasting ? 

(i) Note whether any heat energy has developed, 
as indicated by plates or liquids becoming warmer. 

Carefully space your notes, writing them in columns 
headed Operations, Observations, Inferences, so that 
each operation and its corresponding observations and 
conclusions shall stand out prominently on the page. 

Lessons. — (a) Energy changes. 1. If the elec- 
trodes are tested on open circuit by means of a very 
sensitive electroscope (or electrometer), the + elec- 
trode shows a positive electrostatic charge and the 
— electrode a negative charge. Chemical potential 
energy of zinc and acid has been transformed into 
electrical potential energy. 

2. When the circuit is closed, this is transformed 
into electrokinetic energy, associated with the con- 



MAGNETISM AND ELECTRICITY 151 

ducting wire. 3. This energy can do several kinds 
of work. (What kinds ?) The supply of energy is 
kept up at the expense of zinc and acid as long as 
the circuit remains closed, or until the chemical 
potential energy is exhausted. 

(5) Since the zinc wastes away, and the copper 
does not, it is evident that the chemical change takes 
place at the zinc plate and not at the copper. But 
the hydrogen bubbles originate at the copper plate. 
Therefore we conclude that the chemical action is 
handed along from molecule to molecule through the 
liquid. 

(V) Amalgamating the zinc largely prevents "local 
action," due to iron or carbon particles existing as 
impurities in the commercial zinc. By local action 
chemical energy is transformed into heat in the cell 
and is wasted, instead of being wholly transformed 
into electrokinetic energy, available in the external 
circuit. 

Exercise Number 41 

electro-plating 

Referexces 
A 357, 358, 414, 429-431 H k W 251, 254, 255 

C &C 445-451, 4G4, 472 JJ 57-G7, 90, 145, 153, 155- 

C 297, 29S, 307-309, 321 159, 370 383 

GP 442-445, 451, 452, 463-467, M & T 272 285 

548, 536 T 162, 17s. 190, 212. 236-245, 

GE 307. 313. 322. 333. 371, 377 492 VM\ a 
H 365-370, 382, 393 W & 1 1 279 280, 290 29 1 . 306- 

312 

Purpose. — The purpose of this exercise is to learn 



152 LABORATORY EXERCISES IN PHYSICS 

how electroplating is done, and observe some of the 
phenomena of electrolysis. 

Apparatus. — If an iron object such as an ordinary 
key is to be plated with copper, you must have a 
copper plate like that used in Exercise 40, a battery 
jar containing the plating solution (some salt of 
copper dissolved in water), some source of steady 
current (dynamo, or three Daniell or gravity cells). 
You will need a cleat, like that of Exercise 40, or 
some other convenient device for supporting the 
copper plate and key in the fluid, and some wire 
hooks, connecting wires, and double connectors. 
For cleaning the article to be plated use a plater's 
scratch brush (or any stiff brush with powdered 
pumice stone), and a jar of cleaning acid must also 
be at hand. 

The Dynamo Current, if used, should be regulated by the 
teacher with the aid of a variable resistance, and should be 
distributed to the tables in series i.e. the current should pass 
through the apparatus at each table in succession, not be 
split up among them. 

Cleaning Acid for Iron is made by slowly pouring 15 parts 
of commercial sulphuric acid into 125 parts of water (with 
thorough stirring) in a stone jar, and adding 1 part each of 
nitric and hydrochloric acids. 

Copper Plating Solution for Iron. — (Caution! The 
Cyanides, used in this solution are deadly poisons. Acetate of 
iron is the antidote, but if any considerable quantity were 
swallowed, the patient would probably die. Great care should 
be taken not to get the solution on the hands, as the poison 
will act by absorption through a scratch or even through the 
skin. If the student observes this precaution he is in no 
danger. It is best, however, to make a rule never to touch chem- 
icals of any kind with the hands or to use them in any way in 
which they may be spilled on the floor or tables or clothing.) 



MAGNETISM AND ELECTRICITY 153 

Copper cyanide is first prepared as follows: A solution 
made of 1 part by weight of C. P. (chemically pure) potassium 
cyanide in 16 parts of pure water, is slowly poured, with stirring, 
into another solution, made by dissolving 2 parts of crushed 
copper sulphate crystals in 16 of water. The potassium cyanide 
solution is added until the green cyanide of copper ceases to be 
thrown down as a precipitate. The solution is then poured 
off, and the precipitate washed with water on a filter and dried. 
To make the plating solution, this copper cyanide is stirred 
into a solution made of 4 parts C. P. pota sium cyanide to 32 
parts of water until no more of it will dise jive; and then 1 part 
of the solution of potassium cyanide is added. The solution 
works best if kept warm while plating ,vith it. 

The cleaning and plating solution , should be made by the 
teacher, under the fume hood or oat doors, as the fumes are 
injurious. The solutions should be kept in labeled acid bottles 
when not in use. For the exercise, the cleaning acid is best 
placed in jars, in the sink, where all may use it. 

Cleaning the Object. — If the object is rusty, scour 
it with sand. If it is greasy riu/e it in a hot solu- 
tion of caustic potash. Rub it thoroughly all over 
with the scratch brush, using lengthwise strokes, 
and keeping it wet with water. When it is thor- 
oughly bright at every point, rinse it well with 
water, and soak it for 5 minutes in the cleaning 
acid. Do not lay it doivn or touch if with tlic 
fingers. If you do, the plating will not stick. 
Handle it with pincers or a wire twisted around it. 

Depositing. — Suspend the cleaned article by a thin 
copper wire, which is twisted with a firm, clean 
joint round a heavy copper wire. Place this heavy 
wire in one slot of the wooden cleat, and the copper 
plate in the other. With double connectors, join 
the copper plate [anodt \ with the \r (copper) pole of 
the battery, and the object to be plated (cathocL 



154 LABORATORY EXERCISES IN PHYSICS 

with the — (zinc) pole of the battery. The anode 
and cathode may now be lowered into the jar of 
electrolyte (plating solution). They should be about 
3 inches apart. Watch for the deposit of copper 
which begins to form on the cathode. It should be 
even and firm. If it is dark and powdery, the cur- 
rent is too strong, and should be diminished by 
increasing the distance between the electrodes (anode 
and cathode), or by otherwise adding to the resist- 
ance of the circuit, or by removing a cell. If the 
deposit is crystalline and forms too slowly ? the cur- 
rent is too weak, and another cell should be added 
or some of the resistance removed from the circuit. 

It is better to have two anodes in parallel and 
place the cathode between them. If there is only 
one, the object should be turned around occasion- 
ally. 

With careful attention to these directions, a firm, 
permanent coating of good thickness should be 
obtained in about an hour. If the time allowed is 
too short, or if the deposit does not stick, the clean- 
ing and depositing should be repeated. 

If a very thick deposit is wanted, it will be neces- 
sary first to give the object a very thin coating in 
the cyanide solution, remove and wash it, and then 
to allow it to remain in a plating cell of copper sul- 
phate solution while the current passes for several 
hours. The copper sulphate plating solution is 
made by dissolving 4 parts by weight of crushed 
copper sulphate crystals in 20 parts of pure water 
and slowly stirring in 1 part of sulphuric acid. 



MAGNETISM AND ELECTRICITY 155 

This solution should be filtered and kept clean. It 
is good for copper plating all metals except iron, 
steel and zinc. 

Polishing. — After the object has been plated, it 
should be washed and polished. This is best done 
by rubbing it first with a fine scratch brush or the 
finest emery cloth (always lengthwise), and then 
with a soft cloth and rouge. 

Lessons. — (a) State whether in a general way 
your observations seem to verify the following state- 
ment: 

' * Other things being equal, the amount of metal 
deposited is proportional to the strength of the cur- 
rent, and also to the time during which it passes." 

(b) State why the current is weakened by separat- 
ing the electrodes. 

(c) Give a reason why such extreme cleanliness is 
necessary in order to obtain a permanent deposit. 

(d) What metal should be used as anode, and 
what metal should be in the electrolyte, in order to 
plate with silver ? With nickel ? With gold? 

(e) Describe any other phenomena which you may 

have happened to observe in this experiment. 

Complete Directions for successfully plating all kinds of 
articles, and for electrotyping medals, wood cuts, etc. will be 
found in " Electroplating" by J. W. IVquhart (Van Nostrand, 
N. Y. 1905). 

OPTIONAL PROBLEMS 

(a) Storage Battery.— Cut from sheet lead two elec- 
trodes of t lie same shape as the plates of the simple voltaic cell 

(Fig. 32); scrap'' them clean and bright. Mount them in the 
wooden cleat, and with the double connectors join one lead 



156 LABORATORY EXERCISES IN PHYSICS 

plate through a galvanometer to the -f- pole of a battery of 3 
or 4 gravity or Daniell cells in series, and mark this electrode -)-. 
Join the other lead plate to the pole of the battery, and mark 
it — . Lower the plates into an electrolyte composed of 1 
part by volume of pure sulphuric acid to 10 of water, pass the 
current through the lead cell during 15 minutes to an hour. 
Note the direction of the galvanometer deflection. Xow 
disconnect the wire from the— pole of the battery and touch it 
to that terminal of the galvanometer which was next the -f- pole 
of the voltaic battery. Do you observe a deflection in the 
opposite direction? If so state what is happening with regard 
to the lead cell. Why call it a storage battery? What kind 
of energy went into it while charging? What kind of work 
was done in it? What kind of energy came out of it while 
discharging? See if it supplies energy fast enough to ring a 
bell or operate a buzzer or a telegraph instrument. 

The power of such a cell may be very greatly increased by 
"forming" its plates. This is done by repeatedly charging, 
discharging through a resistance, allowing it to rest for some 
time, and then charging in the opposite direction. After 
forming, it is finally charged for about 30 hours in one direction 
only. After this it should never be entirely discharged and 
should never be charged in the other direction. A quicker 
method of treating the plates is that of "pasting 11 them. To 
do this make a thick paste of minium or litharge ' v oxide of lead) 
and dilute sulphuric acid. Then roughen the plates, by dent- 
ing them all over with a nail or other sharp instrument so 
as to make a multitude of little pockets for holding the 
paste. Spread the paste on firmly with a putty knife, and 
then set up the cell and charge for 30 hours. A cell to be prac- 
tically useful should have six plates, 3 -|- and 3 — , placed 
alternately, and connected parallel by bolts or clamps. They 
must be close together and are to be kept from touching by 
strips of window glass or glass tubing. 

Minium is recommended for the -f- plates and litharge for 
the — plates. 

For full directions for making and operating a practical 
storage battery, cf. School Science and Mathematics, Vol. V, 
p. 268, April, 1905. 

(6) Measuring Current Strength. — Place cleaned and 



MAGNETISM AXD ELECTRICITY 157 

weighed electrodes of copper in filtered copper sulphate solu- 
tion, and pass the current through it for as long a time as you 
have to spare, i.e. not less than 30 minutes. Record the 
time of starting and stopping. Wash the electrodes first in 
water, then in alcohol, dry them over a radiator, and reweigh 
them. By subtraction, determine the amount of metal lost 
by the anode, and the amount gained by the cathode. Theoret- 
ically these amounts should be equal, but practically they are 
seldom found to be so. Divide the gain of the cathode in gm. 
by the time in sec. The result is the amount deposited by 
this current in 1 sec. Since a current of 1 ampere deposits 
0.00032S gm. of copper in 1 sec, the number of amperes in the 
given current will be found by dividing the amount which it 
deposits in 1 sec. by 0.000328. If an ammeter or galvanometer 
was connected in series with the battery and electrolytic cell 
during the passage of the measured current, and if readings 
were taken at intervals, the mean of all the readings will rep- 
resent (on the scale of that particular instrument) the num- 
ber of amperes that were passing. By making other similar 
tests with different steady currents the scale of the galvan- 
ometer may be calibrated or standardised, and marked so as 
to indicate current strength directly in amperes. If the in- 
strument used is a galvanometer, it should be connected with 
a commutator (cf. Appendix F) so that the current may be 
reversed after each reading. This is to eliminate the effect of 
any inequalities in the readings on the two sides of the zero. 



CHAPTER V 

SOUND 

Exercise Number 42 
speed of sound 

References 

A 184 GE 180 J 18, 24, 25, 31 

C 191, 192 GP 157 M & T 311, 312 

C & C 180, 181 H 189-191 W & H 339 

H & W 338 

Purpose. — The purpose of the experiment is to 
determine the speed of sound in open air.* 

Apparatus. — The appliances required are : (#) a 
surveyor's tape, or a bicycle with an accurate cyclom- 
eter attached ; (5) a stop-watch ; (<?) a pistol and 
some blank cartridges ; (cT) two thermometers. 

Place. — This must be such as to furnish a straight- 
away stretch of open ground, level, and uninter- 
rupted by trees or buildings. A country road or 
railroad is best. Such a place can usually be reached 
by a car line or bicycles, even by classes in a large 
city. 

Operations. — (a) Measure off as long a distance 
as is available, — call the two stations A and B. 
They must be half a mile or more apart. If there 
are several bicycles with cyclometers, let all measure 

158 



SOUND 159 

the distance, average the results, and reduce to feet 
by multiplying by 5280. If the school own a sur- 
veyor's tape, let the distance be measured by that 
also, and the result averaged with that obtained by 
the cyclometers. 

(5) Let half the party go to station B, and the 
rest remain at A. Let a person at A set the stop- 
watch, and be ready to start it when he sees the puff 
of smoke from the pistol. When he is ready he 
shows a white handkerchief to the person who is to 
fire the pistol at B. 

(tf) Just before firing, B shows a handkerchief to A. 

(6?) The watch is started at the instant of seeing 
the puff of smoke, and stopped at the instant of hear- 
ing the sound. 

(e) Let different pairs of students repeat the 
operations, the teacher standing near the observer 
and judging each time whether the result of the trial 
is worthy to be recorded. 

(/) Now let the two parties exchange the pistol 
and watch ; and let them make a new set of obser- 
vations equal in number to the first set. The tem- 
perature should be taken several times at each station, 
the thermometer being screened from sun and 
wind. 

Data. — Record in tabular form, the values of the 
distance, Z, and of the time interval, t, observed by 
the first party, and of the time interval, t\ observed 
by the second party, and of the temperature, T. 
Also record the average values of /. /. /', and T. Add 
t and t' and divide; by - to get the mean time interval. 



160 LABORATORY EXERCISES IN PHYSICS 

Calculation. — Since speed = ——. , divide the 

time 

mean value of I in feet by the mean time interval in 

seconds. 

Sources of Error. — Since the time interval is very 
small, and since the percentage error of the result 
cannot be less than that involved in measuring the 
time, the errors in the measurement of I will, there- 
fore, be relatively unimportant. 

The personal equation of the observers will be the 
most serious kind of error, and will be apparent in the 
variation of the individual values of t and t f from 
their averages. Unless the day is perfectly calm, 
the wind will increase the speed of the sound if 
travelling with it, and diminish the speed of the 
sound if travelling against it. 

This effect will be at least partially eliminated by 
observing at A and at B alternately. On account of 
the shortness of the time, the instrumental errors of 
the watch may also be serious. If the watch can be 
rated by reference to an accurate clock, the necessary 
corrections may be applied. 

Temperature Correction. — Reduce the observed 
value of the speed of sound to what it would be at 
0° C. by subtracting two feet per second for each 
degree that the observed temperature is above zero 
(S =S t -2f). 

Lesson. — This exercise illustrates the early 
methods of determining the speed of sound. In 
later methods the time of starting and arriving have 
been automatically recorded by means of the electric 



SOUND 161 

current upon a sheet of paper moved by clockwork 
(chronograph.) Thus the personal equation is 
nearly eliminated. 

Exercise Number 43 

vibration frequency of a tuning-fork 

References 

A 192-198, 201 GP 173-176 M & T 318, 321, 

C 199, 212, 213 H 186, 206-212 322, 332 

C & C 204-208, 226 H & W 335, 344 W & H 344 

GE 174, 192-194 J 7, 9, 39 

Purpose. — The purpose of this exercise is to rate 
a tuning-fork, or, in other words, to determine the 
number of vibrations which it makes in one second. 

Apparatus. — A pendulum and a fork are mounted 
on supports fixed to a long board, so that, when they 
are vibrated simultaneously, the styluses that are 
attached to them will trace lines very near together 




Fig. 33. — Apparatus for ratings tuning-fork. 



162 LABORATORY EXERCISES IN PHYSICS 

along a strip of smoked glass. When the glass is 
drawn swiftly along the board each stylus traces a 
wavy line, and the line traced by the pendulum 
crosses and recrosses the line traced by the fork. 
The height of the fork above the glass, and also that 
of the pendulum, is adjustable by means of a clamp 
or screw so that the point of each stylus can press 
very lightly against the glass. A piano-hammer or 
a little mallet of soft wood is used to set the fork 
and pendulum to vibrating. 

Operations. — (a) Rate the pendulum as described 
in Exercise 1, page 1. Record three ratings, and 
take their average as the number of vibrations made 
in one second by the pendulum. 

(6) On a block of wood ignite a lump of camphor 
about the size of a pea, and, holding the glass hori- 
zontally about a half-inch above the burning cam- 
phor, move it slowly backward and forward until its 
under surface is entirely covered witli a thin layer of 
soot. 

(<?) Now lay the glass on the board, blackened 
side up. The styluses should be lifted when doing 
this, so that they will not be bent out of their 
positions. The styluses should now press very 
lightly against the smoked glass near its end. See 
that the glass rests in such a position that it may be 
quickly pulled along the board in the direction of its 
length, so as to allow the fork and pendulum to trace 
their vibrations on it while it is moving. The speed 
with which the plate ought to be moved must be 
learned by practice, and is twice as great for a fork 



SOUND 163 

making 256 vibrations as for one making 128 vibra- 
tions. (Why ?) 

(c7) Set the fork and pendulum to vibrating, and 
slide the plate. 

If the trial is successful, a set of tracings like 
Fig. 34 will be obtained. It is well to get at least 
two good traces on the plate. 

Each of the spaces, a<?, bd, ce, df, etc., represents 
the time occupied by one vibration of the pendulum. 
(Why ?) Also each space from crest to crest or from 




Fig. 34. — Showing the appearance of the smoked glass after taking 
the tracings. 



trough to trough of the w 7 avy line traced by the fork 
represents one complete vibration of the fork. Count 
the number of vibrations and tenths of a vibration of 
the fork traced between a and e, c and g, e and g, 
and so on. Make and record at least three different 
counts. The average of these counts is the number 
of vibrations made by the fork while the pendulum 
makes one vibration. 

Data. — Tabulate the numerical data. 

Let n be the number of complete vibrations which 
the fork makes while the pendulum is making one 
complete vibration ; let N p be the number of complete 
vibrations made by the pendulum in one second, and 



164 LABORATORY EXERCISES IN PHYSICS 

let ]V f be the number of complete vibrations made by 
the fork in one second. 

Then N f = N p xn. (Why ?) 

A much more accurate method of treating the observations 
is to count the whole number of vibrations and the fraction of 
a vibration that were made by the fork while the pendulum made 
three or more vibrations. Divide the former number by the 
latter to get the n of the above formula. In making the count 
it is well to mark on the glass every tenth vibration of the fork. 
The difficulty in applying the method suggested above lies in 
the fact that it is hard to get a good trace of the required 
length with the apparatus usually supplied. 

Sources of Error. — Qa) Since the two styluses are 
necessarily a little distance apart, errors will arise from 
changes in the speed of the plate during its motion. 

(5) Errors are involved in estimating the fractions 
of a vibration. 

(<?) What errors are involved in rating the pen- 
dulum ? 

Lessons. — (a) From a table of the notes of the 
standard scale and their corresponding vibration 
numbers, choose that note to which the vibration 
number of the fork that you rated most nearly 
agrees ; and call this the note given by the fork. 

(5) See if the fork is in tune with the corre- 
sponding fork of a standard set by sounding them 
together and listening for " beats." 

(c) Compare the notes given by this fork and 
another of different frequency which has been rated 
by another student, and state what effect the vibra- 
tion frequency of a sounding body has on the note 
given out by it. 



?QTJND 



165 



Exercise Number 44 



WAVE LENGTH OP A TONE 



A 205 
C 173, 174 
C & C 191-194 



References 

GE 187-189 
GP 168-170 
H 198-202 



J 56, 58, 61, 62 
M & T 292-296, 299, 
301, 314, 323, 324 




Purpose. — It is proposed to determine the wave 
length of the tone given out by a tuning-fork. 

The method consists in measur- 
ing the length of the air column 
that will give resonance to the fork 
and in deducing therefrom the 
length of the waves. 

Apparatus. — (a) The tuning-fork =^ 
should be one making not less than 
256 vibrations, and preferably the 
one whose vibration number has 
been determined in the preceding 
exercise. 

(7>) A glass tube not 
less than eighteen inches 
long, and having an inside 
diameter of not less than 
an inch, is mounted on a 
suitable support and pro- 
vided with a convenient 
f means of varying the 

!i length of the column of 
Fiq. 35. air contained in it. 



_J 



Fiq. 36. 



166 LABORATORY EXERCISES IN PHYSICS 

Two very convenient forms of apparatus are shown 
in Figs. 35 and 36. Water is used as a piston, its 
level in the tube being easily and accurately adjusted 
in the manner suggested by the illustrations. 

Operations. — Qd) Set the fork in vibration by 
striking it with a piano-hammer, or a little mallet 
made of soft wood, and place it close to the mouth of 
the tube in such a position that one of the prongs exe- 
cutes its vibrations in the line of the axis of the tube. 

(J) Make the air column evidently too short, and 
increase its length until a strong resonance occurs. 

(c) By repeated trials test the adjustment, and 
try to fix it between definite limits. 

(tT) When satisfied that the length of air column 
corresponding to maximum resonance has been fixed 
within the smallest limit, record the amount of this 
limit, and, with a rule, measure and record the length 
of the air column, i.e. the distance from the water 
to the end of the tube. Repeat the operations as 
many times as the time will permit, and record all 
the observations in tabular form. 

Calculations. — Take the average of the numbers 
representing the length of the resonant air column. 
Theoretically, this is \ the length of the wave, but 
experiments have shown that the diameter of the 
tube affects the length of the resonant column. A 
correction equal to \ the internal diameter of the 
tube should be added to the mean length of the 
latter as determined above. 

The wave length of the tone given out by the fork 
is then obtained by multiplying the corrected length 
by 4. (Why?) 



SOUND 167 

Resonance occurs when the ah' column is f or J the wave 
length, but these cases are not here considered. 

Sources of Error. — The most important error is 
that involved in the judgment of the observer as to 
when the loudest resonance occurs. State the dis- 
tance through which the piston had to be moved each 
way from the position for maximum resonance before 
the sound became unmistakably fainter. What per 
cent is it of the length of the column ? The percen- 
tage error of the result cannot be less than this unless 
the mean of a long series of observations is taken. 

Lessons. — (a) This exercise is intended to famil- 
iarize the student with the theory of resonance, and 
afford practice in a simple method of directly deter- 
mining wave length. 

(b) Since a wave traverses a distance equal to its 
own length during one complete vibration, it is clear 
that the velocity of sound or the distance traversed 
in one second = wave length x vibration frequency. 
Calculate the velocity of sound from the wave length 
and the vibration frequency of the fork. Compare it 
witli the velocity obtained in Exercise ±2. In order 
to compare them, the units of length must, of course, 
be the same, and both values must be reduced to 
what they would be at 0° C, as in Exercise 42. 

Knowledge of wave lengths and of the various methods of 
measuring them is of little direct practical value, bid has proved 
to be immensely important in developing the theory of air waves 
and ether waves. In consequence of this theoretical knowledge 
musical instruments have reached increased perfection; and the 
discovery of wireless telegraphy became possible. 



168 LABORATORY EXERCISES IN PHYSICS 

Exercise Number 45 
cause op overtones 

References 

A 199, 200 H 221, 223-225 

C 200, 209 H & W 336 

C & C 210, 211, 213-215, 220-222 J 54-55 

GE 195, 197 M & T 299-301, 317, 
GP 179-182, 185, 186 327-332, 337-345 

Purpose. — The purpose of this exercise is to de- 
termine the positions of the nodes and segments of a 
musical string when vibrating under certain condi- 
tions, and to investigate the relations of these nodes 
and internodes to the overtones given out by the 
string. 

Apparatus. — A sonometer, which consists of two 
piano wires stretched over a pair of frets at the ends 
of a suitable sounding-board. The wires pass over a 
fixed bridge near one end and differing tensions may 
be applied to them by means of weights or spring 
balances. A movable bridge is also provided. If the 
tensions are applied by means of weights, pulleys 
or levers shaped like the quadrant of a circle, are used 
to change the direction of the forces from horizontal 
to vertical. 

A violin bow, a cake of rosin, and a number of 
bent paper strips, to be used as riders, are also 
required. 

If no sonometers are available, the wires may 
be stretched over the laboratory table ; and wooden 



SOUND 



169 



wedges placed thereon take the place 
of the bridges. If spring balances are 
used, they may be so arranged that 
the tensions can be accurately adjusted 
by means of a pair of long screws 
which pull in the lines of the wires. 

Part A 

Operations and Observations. — (a) 

See that the sonometer is securely 
fastened to the table by means of a 
clamp or handscrew, and that the ten- 
sions draw the wires in horizontal 
lines parallel with the length of the 
sounding-board. The wires should 
rest but lightly on the frets that are 
next the stretching forces. 

(b) Insert a movable bridge so that 
the length of one of the wires between 
the two bridges shall be (say) one meter. 
Now bow the wire near (iiot at) the 
middle. Can you see the part between 
the bridges vibrating as a whole ? 
Apply such a tension as will cause the 
wire to give a full round note. Drop 
paper riders so that they will bestride 
the wire at several points along its 
length. What happens to the riders? 
What does this indicate about the 
condition of the wire at the places 
where the riders were placed ? 




w 



170 LABORATORY EXERCISES IN PHYSICS 

By repeated trials ascertain whether there is any 
part of the wire that is not in vibration when it has 
been bowed or plucked near its middle point. 

(e) Carefully listen to the tone and try to keep it 
in mind. It is called the fundamental tone of this 
string, with the given length and tension. State 
whether the string vibrates as a whole when it gives 
its fundamental tone. Where are the nodes, or sta- 
tionary points ? Illustrate the condition of the string 
and the behavior of the riders by a diagram. Write 
" Fundamental " beneath the diagram. 

(cT) Place riders at the ends and at the three 
points which divide the string into fourths. Call 
the riders and the points at which they are placed 
0, ^, J, f, and 1. Now press, not too heavily, with 
the finger upon ^ and apply the bow near 0. Imme- 
diately after the bow is removed, remove the finger 
also. Which riders remain quiet and which are 
agitated? Repeat until sure that certain riders 
remain quiet wdiile certain others are violently dis- 
turbed. State the conditions of the points of the 
string where the riders had been placed. Illustrate 
by a diagram as in (c). Mark the nodes on the 
diagram. The vibrating parts between the nodes 
are called internodes or segments. Mark them also 
on the diagram. 

(e) Repeat the operation once more and listen to 
the note given out by it. Compare it carefully with 
the fundamental by sounding first one and then the 
other. (To sound the fundamental, you have only 
to remove the finger from the point J.) Is it the 



SOUND 171 

octave of the fundamental ? If so, make another dia- 
gram and write " Octave " beneath it. 

(f) Place riders at points 0, i, J, 1 |, |, and 1. 
Repeat the former operations, but damping with the 
finger at I and applying the bow at point near 0. 
Make sure of the positions of the nodes and segments 
before trying the next case. Illustrate by diagram 
as before, marking nodes and segments. 

((/) Listen to the tone given out by the string 
when vibrating as it does in this case and compare 
it with the fundamental and the octave. Is it the 
fifth (or sol) above the octave ? If so, write " Fifth 
above the Octave" under the diagram. 

(/*) Place riders at points dividing the string into 
eighths and make experiments similar to the preced- 
ing. Damp at -\ and bow near 0. 

Illustrate by diagram as before, marking nodes and 
segments. 

(i) Compare the resulting tone with the funda- 
mental and first octave. Is it the second octave ? 
If so, write "Second Octave" beneath the diagram. 

Part B 

(a) Bow the string (without damping) near the 
point 0. and listen carefully to the note. Can you 
detect the octave, the fifth above the octave, or the 
second octave sounding along with the Fundamental? 
If you arc sure that you can detect any of these, 
record the fad. 

(I>) How near and afterward damp the wire by 
touching it very lightly with a feather or a bit of blot- 



172 LABORATORY EXERCISES IN PHYSICS 



ting-paper at \. Does the fundamental cease ? Do 
you hear the octave ? If so, record the fact. Can 
you infer from this that the octave and the funda- 
mental were sounding at the same time before the 
wire was damped at |- ? Was the wire vibrating as 
a whole and in halves at the same time ? Why did 
the octave come out more clearly after damping ? 

(e) Bow near and damp with the feather at ^. 
Does the fundamental cease ? Do you hear the fifth 
above the octave ? Can you make inferences similar 
to those of (5) ? State them. 

(cT) Bow near and damp at ^. Make a set of 
observations and inferences similar to those made in 
(5) and (V), but applying to the second octave and 
four vibrating parts. 

Data. — Copy the tabular form and fill the blanks. 



Point where bowed 


i 

2 





? 


9 


Point where damped 


— 


i 

2 


? 


? 


Number of nodes 


2 


3 


? 


? 


Number of segments 


1 


? 


? 


9 


Resulting tone 


Funda- 
mental 


Octave 


? 


? 



Inferences. — (a) State whether from your experi- 
ments you are justified in inferring that a string or 
wire can vibrate as a whole and in parts at the same 
time. 



SOUND 173 

(5) State the number of vibrating parts or seg- 
ments which correspond to fundamental, the octave, 
the fifth above the octave, and the second octave, 
respectively. 

(<?) Define an overtone. 

(d) When the tones mentioned in (5) are present 
as overtones, what is the cause of their presence along 
with the fundamental ? 

(e) State whether or not you can discern any 
difference in the quality of the tone, first when the 
overtones accompany the fundamental, and then when 
they do not accompany it. 

Exercise Number 46 

laws of vibrating strings — length 

References 



A 209, 210 


C & C 210-212 


H 220-222 M & T 298-301 


C215 


GE196 


H & W 339 317-320, 335 




GP179 


J 50-53 336 



Purpose. — The purpose of the experiment is to 
verify the law for the relation of the length of a 
stretched string to its vibration number. 

Apparatus. — This is the same as that used in the 
preceding exercise. A second movable bridge is 
necessary. 

Operations. — (a) Adjust the movable bridge so 
that the vibrating part of one wire, -A, is (say) one 
meter long, and increase the tension until the wire, 
when bowed or plucked near the iixed bridge, gives 



174 LABORATORY EXERCISES IN PHYSICS 

a good clear note. Call this note do v and adjust the 
tension and length of the other wire, B, so that it 
gives the same note. It is to be used for reference. 
Students who have studied music will tune the two 
strings to unison without difficulty.. Those who have 
not trained musical ears can tune the second string 
until they begin to hear beats, and then cautiously 
shift the bridge or change the tension until the beats 
can no longer be heard. While the two strings are 
sounding together, as unison is approached, the beats 
diminish in number. 

(£) Move the bridge under A to such a point as to 
make the length of the vibrating part exactly -| what 
it was at first, and sound A and B successively. 

If necessary, hold the wire against the movable 
bridge by pressing lightly against it with the finger 
at a point just outside the bridge. 

Repeat several times. Do you recognize the inter- 
val known in music as do x -mi x (major third) ? If 
so, record it. If the two strings do not seem to give 
this interval accurately, restore the bridge to its 
original position, and test the two strings to see if 
they are in tune, then repeat the operation. 

(c) By means of the movable bridge reduce the 
length of the vibrating part of A to | of its original 
length, and repeat the previous operations. Is the 
interval do x -sol x (major fifth) ? Test as before. 

Leaving A of the length to sound sol v carefully 
tune B to unison with it (by means of its movable 
bridge). Now make the length of the vibrating part 
of A exactly -| what it was at first, and observe the 



SOUND 



175 



musical interval as before. Is it sol 1 -do 2 ? If neces- 
sary, make sure by testing the two wires for unison 
when sounding soI v and repeating the observation. 

(d) If time permits, tune B to unison with A at 
do v and then reduce the length of A to ^. Observe 
and test the interval as in the previous operations to 
learn if the interval is do^-sol^. 

Data. — Tabulate results as follows, appropriately 
filling the blanks : — 



Length 


100 cm. 


so 


66.66 


50 


33.33 


Length ratio : 
New length 

Original length 


1 


4 
3 


2 
3 


l 

2 


l 

3 


New note 


do 1 


? 


? 


9 9 


Interval 


Unison 


') 


9 


9 


Octave 
+ fifth 


Vibration ratio of 
interval : new 
note to funda- 
mental 


1 


5 

4 


9 


9 


9 

1 



Sources of Error. — Errors may arise from unob- 
served changes of adjustment, but the most serious 
error, of course, lies in the judgment of the hearer as 
to the accuracy of the interval. This experiment 
may be performed with much greater accuracy and 
completeness by using one string and a sel of stand- 
ard forks of known vibration numbers, and tuning 
the string to unison with each fork in turn by chang- 



176 LABOBATOBY EXEBCISES IN PHYSICS 

ing the length only. The lengths and vibration 
numbers can then be directly compared. This 
method, however, is not adapted to the equipment of 
most elementary laboratories. 

Inferences. — Compare the ratio between each new 
length and the first length with the ratio between 
the vibration number of the corresponding new note 
and the fundamental. What must be done with each 
ratio of the vibration numbers in order to make it 
equal to the ratio of the corresponding lengths ? 
State the relation of the frequencies of the notes to 
the corresponding lengths of the string. This is 
sometimes called the First Law of Vibrating Strings. 

Exercise Number 47 
laws of vibrating strings — tension 
References. — These are the same as those for Exercise 46. 

Purpose. — The law that states the relation of 
tension of a string to the vibration number is to be 
verified. 

Apparatus. — The apparatus used in Exercises 45 
and 46 is to be used in this experiment. 

Operations. — (a) The two wires are put under 
tensions of about two or three pounds each. The 
tensions should be made as nearly as possible exactly 
equal. The movable bridge is then adjusted under 
both wires at such a distance from the fixed bridge 
that the vibrating parts of the two wires are of equal 
length. If the tensions and lengths are exactly equal, 



SOUND 177 

and the diameters and materials of the two wires the 
same (as they should be), the two wires when sounded 
together will be in unison. 

If beats are noticed, go carefully over the adjust- 
ments of length and tension until these adjustments 
are correct and the two wires are in tune. 

(b) Increase the tension of the wire A until it is 
four times as great as before. If using the spring 
balances, do not forget to allow for the zero correc- 
tion as in Exercises 10 and 11. Is the resulting note 
the octave of the first ? Sound B and A successively 
and compare the notes. By means of a movable 
bridge make B half its original length, so that it 
will give the octave of the first note. Are the two 
strings again in unison ? If not, go over the adjust- 
ments of tension of A and length of B, see that they 
are correct, and try again. If the two strings are not 
in exact unison, is the difference too large to be 
ascribed to such errors as are likely to exist in the 
adjustments of tension ? 

(<?) Restore the two wires to their first condition 
and repeat all the operations, using a tension on A 
which is nine times as great as the first. Is the note 
sounded the fifth above the octave? Make B one- 
third its original length, and test carefully as before 
to see if the two strings are in unison. 

Data. — Call the fundamental do v the octave do 2 , 
and the fifth above the octave sol 2 . Tabulate the 
data. If the number of vibrations per second when 
do l is Bounded is //. then that corresponding to do 2 
is 'In. What is that corresponding to %ol^ ? 



178 LABORATORY EXERCISES IN PHYSICS 

Inference. — (a) Compare the tensions and the 
corresponding vibration numbers. What has to be 
done with the former in order to make the latter 
proportional to them ? 

(&) State the law that is verified by the observa- 
tions made in this exercise. 

Exercise Number 48 

laws op vibrating strings — diameter 

References. — These are the same as those for the two 
preceding exercises. 

Purpose. — The law of the relation of vibration 
number to diameter is to be verified. 

Apparatus. — This is the same as in the three pre- 
ceding exercises, except that the two wires used 
should have diameters which bear a simple relation 
to each other. If Nos. 22 and 28 B. & S. gauge are 
used (or 18 and 24), the diameters will be very nearly 
as two to one. A vernier caliper or micrometer 
caliper is needed for determining these diameters. 

Operations. — (#) By means of the movable bridge 
and a suitable tension, adjust the larger wire, A, so 
that it gives a clear note. Make the length and ten- 
sion of the smaller wire, B, exactly the same, and care- 
fully compare the two notes. Is the note given by 
B the octave of that given by A ? If not, go over 
the adjustments carefully. 

(J) Make A one-half the original length, and see 
if the two notes are in unison. Test the adjustment 
as in the previous experiments. 



SOUND 



179 



(<?) Measure the diameters of the two wires. 
Data. — Tabulate under the following heads : — 



Diameter 



B 



Xote 



do, 



Frequency 



Ratio Frequency .4 = , 
Frequency B 



Ratio Dimeter A = , 
Diameter B 



Sources of Error. — Briefly state the principal 
sources of error. 

Inferences. — (a) What must be done with the ra- 
tio of the frequencies in order to make a proportion 
with the ratio of the diameters ? 

(J) Can the lack of exact proportionality be fairly 
ascribed to experimental errors ? 

(<?) State the law verified in the observations. 

(c7) Other things being equal, what is the relation 
of diameter to mass per unit length ? 

( Mass j = volume A x density = J it x (diameter ,) 2 

x 1 X density, and mass^ = volume 7i x density = \tt 

X (diameter j) 2 x 1 x density. 



Iliads, 



massj 

What, then, is the relation of the vibration numbi rs 
of two strings to their masses per unit length f 

Try to find and understand applications of the laws of 
vibrating strings in various musical instruments* 



CHAPTER VI 



LIGHT 

Exercise Number 49 

bunsen's photometer. law of inverse squares 

References 



A 267, 268 


GP 286-288 


J 7-10 


C & C 238 


H 447-449 


M & T 376 


GE 223-225 


H & W 276 


W & H 366 



367 

Purpose. — The purpose of this experiment is to 
verify the law of inverse squares for light by the 
method of Bunsen's photometer. 

Apparatus. — The photometer consists of a meter 
rule and three square blocks, each of the same thick- 
ness as that of the rule. The blocks can slide along 




A 
Fig. 38. 



B C 

- Simple form of Bunsen's Photometer. 



the table beside the rule, whose face is just flush with 
their upper surfaces. Each block has a pair of 
diameters accurately scratched upon its upper surface 

180 



LIGHT 181 

by means of a knife and square. One of the blocks, 
i?, carries a pair of uprights, to which a screen of 
white paper may be attached by bits of soft wax, the 
centre of the screen being over the centre of the 
block. At the centre of this screen is a circular 
grease-spot (made by driving into it, with a hot 
flatiron, a bit of paraffin). One block, A, carries a 
single candle at its centre, and the third, (7, a row of 
four candles set close together, two on each side of 
the centre of the block. The centres of the candles 
are on the diameter of the block, that is, perpen- 
dicular to the length of the rule. Shallow holes are 
bored into the blocks to receive the candles. The 
apparatus should be used in a thoroughly darkened 
room, and screened from the light of the other tables, 
or, better still, enclosed in a long box with chimneys 
at the ends, and with doors or opaque cloth curtains 
on the side toward the observer. With this latter 
arrangement the room need not be absolutely dark. 

Operations. — (a) See that the five candles are all 
of the same height, and that their wicks are trimmed 
and bent down slightly, so that they give flames as 
nearly as possible of the same size. Trim them if 
necosary. 

(b) Place the blocks A and against the rule near 
its opposite ends. 

((?) Slide the block B along the rule until the 
grease-spot ceases to be visible when seen from a 
point a little to the right of the edge of the screen, 
and read on the rule the position of the knife scratch 
upon which the screen rests. 



182 LABORATORY EXERCISES IN PHYSICS 

(d) Now make a second setting in precisely the 
same manner, observing the spot from a position as 
far to the left of the edge of the screen as the first 
point of observation was to the right of it. Read on 
the rule the position of the knife scratch correspond- 
ing to the disappearance of the spot. Record the 
average of these two settings as the mean position of 
the screen. 

(e) Read the positions of the knife scratches on 
the blocks A and (7, and record them as the positions 
of the two lights. By subtraction determine the 
distances of the two lights from the screen. 

(/) Change the position of one of the lights, and 
repeat the settings. Make as many pairs of readings 
as the time permits. 

Data. — Record the results of each setting in a 
column, each result opposite its proper heading. 

Numerical Data 



Trials 






Headings, scratch A 






Readings, scratch C 






Readings, scratch B right 






Readings, scratch B left 






Readings, scratch B mean 







LIGHT 



183 



Numerical Data — Continued 



Distance A B 






Distance CB 






Ratio — 
AB 






Light emitted by A 


1 




Light emitted by C 


4 





Sources of Error. — State the errors which may be 
due to (a) the candles ; (5) the position of the ob- 
server, and his judgment ; (e) light received by the 
screen from sources other than the direct rays of 
the candles. If all extraneous light be not excluded, 
the results will be thoroughly unreliable. 

Inferences. — We assume that when the spot dis- 
appears at the mean position of the screen, the two 
surfaces are illuminated with equal intensities. 

(a) If four candles, at distance CB, give the same 
illumination to the screen as one candle does at dis- 
tance AB, what is the intensity of illumination by 
one candle at CB as compared with that by one 
candle at AB > 

(5) What must be done with the ratio of the 

distances — in order to make it equal to the ratio 
a l B 

of the intensities with which one candle illuminates 

the screen at these two distances respectively. (Both 
ratios should be reduced by performing the indicated 



184 LABORATORY EXERCISES IN PHYSICS 

CB 

division.) If there is a decimal remainder to——-, can 

AB 

it fairly be ascribed to experimental error? State 
the law that is verified in this case. 

Additional Work. — If the time assigned admits of further 
work, the four candles may be replaced in turn by three, two, 
and one, and the settings repeated. In this case, although it 
will not be so obvious, the ratio of the squares of the distances 
will be equal to the ratio of the number of candles used, 
as before. 



Exercise Number 50 
Alternative Method 

RUMFORD'S PHOTOMETER. LAW OF INVERSE 
SQUARES 

References 



A 267, 268 


GP 286-288 


J 7-9 


C & C 235-237 


H 441-149 


M & T 376 


GE 223-225 


H&W276 


W & H 366 



Purpose. — In this exercise, the principle of Rum- 
ford's photometer is to be used to verify the law of 
inverse squares. 

Apparatus. — A white cardboard screen is tacked 
to a block so as to make the card stand upright. 
Two square blocks, A and i?, have their diameters 
marked or scratched on their upper surfaces, and are 
to be used as carriers for five equal pieces of candle. 
With chalk or pencil a perpendicular is drawn to the 
screen at its middle point. On this perpendicular, 



LIGHT 



185 



at about 5 cm. from the screen, is mounted a small 
cylindrical rod. (A penholder or a lead pencil stuck 
into a flat cork will do.) Through the axis of the 
rod are drawn two straight lines, pq and rs, making 




Fig. 39. — Rumforcl's Photometer. 

equal small angles with the perpendicular and meet- 
ing the screen. On the perpendicular is placed a 
second cardboard screen, so as to shield the two lights 
one from the other. 

Operations. — (a) At the centre of the block A 
mount one of the candles, and along the diameter of 
B mount the other four candles close together, and 
one behind another. 

(J) Light the candles, bend the wicks down a little, 
and let them burn for a few moments till their flames 
are of equal size. If necessary, trim them to make 
them so. 

(<?) Move A along with a diameter on the line pq 
until the axis of the candle is, saw 25 cm. from the 
screen. Move the diameter of B along the line r«, 
and note the two shadows of the rod which are caused 



186 LABOBATOBY EXEBCISES IN PHYSICS 

by the two lights. If the black parts (umbras) of 
these shadows are not close together, move the screen 
toward the rod until they are. 

(d) Now, with the greatest possible care, slide B 
backward or forward along rs, as may be necessary, 
until it is in such a position that the two shadows 
appear equally dark. 

(e) Test the sensitiveness of the adjustment by 
moving the block forward or backward until each 
shadow in turn is manifestly less dense than the 
other. Record the amount of the change in distance. 
This represents your personal equation, or the dis- 
tance within which you can set with certainty. 

(/) Measure and record the distance from the 
screen to the middle of the line of four candles. Do 
this by measuring to the end of the block and adding 
half its diameter. 

(#) Place the candles so that the line joining their 
centres is perpendicular to rs and is bisected by it. 
Repeat (6?), (Y), and (/). 

(A) Change the one candle to a distance of, say, 
40 cm. from the screen, and repeat all the previous 
operations. 

Data. — Record the quantities opposite their proper 
headings. Make a vertical column for each setting. 

Sources of Error. — State how errors may arise (a) 
in setting, (5) in reading distances, (e) in assuming 
that the candles radiate equal amounts of light. 

Inferences. — We assume that when the shadows 
are equally black the screen is equally illuminated 
by the two lights. 



LIGHT 



187 



Numerical Data 



Settings 


1 


2 


Distance pA 






Distance rB 






Eatio — - 
pA 






Light emitted by A 


1 




Light emitted by B 


4 





(a) If four candles at the distance rB give the 
same illumination to the screen as one at distance pA, 
what is the intensity of the illumination by one can- 
dle at rB as compared with that by the one candle 
at pA? 

(J) What must be done with the ratio of the dis- 

rB 

tances — - in order to make it equal to the ratio of 
pA 

the intensities with which one candle illuminates the 
screen^ at these two distances respectively ? (Reduce 
both ratios to their lowest terms, expressing that of 
the distances as a mixed decimal number, if neces- 
sary.) 

(V) Can the decimal remainder be fairly ascribed 
to experimental errors ? 

(c?) If so, state the law that has been verified by 
your results. 



188 LAB OR A TOR Y EXERCISES IN PHYSICS 

OPTIONAL HOME WORK 

Shadow Method. — Prepare 3 squares of stiff pasteboard, 
a 1 inch, b 2 inches, and c 6 inches on a side, and block their 
areas off in square inches. The screens may be supported by 
knitting needles stuck in blocks of wood. Place a tin screen 
with a small hole in it just in front of a candle flame so as to 
have your source of light reduced nearly to a point. Place a 
6 in. in front of the source, and move b to where a's shadow 
just covers it; then remove a, and see that all the light which 
fell on it now falls on b. Their areas are as 1 to 4: how do 
their intensities of illmuination compare? Measure their dis- 
tances from the source and compare the ratio of their illumi- 
nations with that of their distances. Do the same with a and c. 
Do your experiments verify the Law of Inverse Squares? 

Rumford's or Bunsen's Photometer methods may easily 
be used at home, with materials that are found in every 
household. See Light, by Mayer and Barnard. (Appleton's, 
N.Y.). 

Exercise Number 51 

photometry. candle power of a lamp 

References. — These are the same as those for Exercise 49. 

Purpose. — It is proposed to apply the law of in- 
verse squares in measuring the candle power of a 
lamp by the method of Bunsen's photometer. ' 

Apparatus. — In addition to the Bunsen's photom- 
eter, a kerosene lamp, gas burner, or incandescent 
electric lamp is supplied, also a small block or adjust- 
able support for the candle, by means of which it 
may be raised so that the centre of its flame shall be 
at the same level as that of the lamp. 

Operations and Data. — (a) Support the candle 
exactly over the centre of block A and the lamp over 



LIGHT 189 

that of B. Trim the candle wick, and elevate the 
candle till its flame is level with that of the lamp. 

(J) Make several pairs of settings exactly as in 
Exercise 35, tabulating the readings and distances as 

before. Record also the ratios ; J . Perform the 

(ABy 

division for the result of each trial and tabulate the 
results. Record the average of these results' as 
the candle power of the lamp. By reference to the 
law of inverse squares and the previous exercise, 

( CBY 
explain why the ratio p y 2 represents the candle 

power of the lamp. ^ ^ 

Lesson. — This is an example of a kind of physical 

measurement which has an extensive application in 

every lamp factory and gas works. 



Exercise Number 52 

regular reflection 

References 

A 260-274 GE 227 J 15-19 

C 330-331 GP 291, 292, 295 M & T 356-359 

C & C 239 H 450-452 W & H 369 

H & W 283 

Purpose. — It is proposed to verify the law of iv- 
flection of light. 

Apparatus. — The appliances needed are: (a) a 
small rectangular piece of plane mirror, fastened by 
rubber bands to a bridge nut or rectangular block ; 
(6) several pins ; (<?) a rule ; (d) a protractor. 



190 LABORATORY EXERCISES IN PHYSICS 




Fig. 40.- 



■ Showing how the mirror and pins 
are to be set up. 



Operations. — (a) Near the inner margin of the 
note-book page, which should be held by weights so 

as to be perfectly 
flat, draw a fine 
straight line, 
MM', and place 
the edge of the 
silvered surface 
of the mirror 
exactly upon it. 
(5) Near the 
outer margin of 
the page, and a 
few centimeters 
to one side of the middle of MM 1 , stick a pin, i v 
which may represent a luminous object and will be 
reflected in the mirror. 

(<?) On the other side of the middle of MM', and 
near the mirror, stick another pin, r v 

(c?) Now place the eye on a level with the page 
and sight along the line between the point r x and 
the point i 2 where the image of the pin i x appears 
to enter the reflected page. 

(e) When the right position for the eye is accu- 
rately determined, stick another pin, r 2 , into the 
page, near its outer margin, in such a position that 
it will exactly hide both the pin r x and the image, 
i 2 , of the pin i v 

(/) Remove the mirror, and with the rule draw 
the line r 2 r v producing it until it intersects MM f . 
Mark the point of intersection, p. Also draw the 



LIGHT 



191 



line i x p. Then will pr 2 represent the reflected 
ray, p the point of reflection (and also of incidence), 
and i x p the incident ray. 

(#) At p erect a perpendicular to the line MM\ 
and call it pq. Now, i Y pq is the angle of incidence 
and qj)r 2 is the angle of reflection. Are they in the 
same plane? Measure them with the protractor. 

(A) Repeat the experiment as many times as you 
can during the laboratory period. Use the same po- 
sitions of the mirror and first pin, but other points 
for the second pin, so as to get different pairs of 
angles. Employ the same letters for the points ; but 
use a different style of lettering for each trial. 

Data. — Record results in tabular form. 



Data 



Trial 


Angle of Incidence 


Angle of Reflection 


Error 


Per Cent 
Error 

































Precautions — Sources of Error. — See that the mirror 
does not get displaced from the line, MM f . Draw 
fine lines exactly through the pinholes. Sight along 
the points of the pins just at the surface of the page. 
Errors may arise from lack of planeness in the mirror, 
inaccuracy in placing pins and drawing lines, and in 
measuring the angles. 



192 LABORATORY EXERCISES IN PHYSICS 

Inference. — -State the law that your experiments 
have verified. 

Exercise Number 53 
image in a mirror 

References 

A 275, 276 GE 229-236 J 20-22 

C 331, 332 GP 296, 297 M & T 356-359 

C & C 242-245 H 453-455 W & H 370-372 

H & W 284 

Apparatus. — The appliances are the same as those 
in the preceding exercise. 

Operations. — (a) Draw the line MM 1 across the 
middle of the note-book page, and place the mirror 
upon it precisely as in Exercise 52. 

(6) Near a lower corner of the page draw an arrow 
about 4 cm. long, making an angle of about 60 de- 
grees with MM 1 , letter its extreme points i x and I v 

(<?) Proceeding exactly as in Exercise 52 ? locate as 
accurately as possible three reflected rays from t, and 
produce them behind MM! , by dotted lines, until 
they intersect one another; obviously they should 
meet in a common point, i v which is the image of 
the point i v This point was sighted at in Exercise 
52, but was not definitely located, because the lines 
of the reflected rays were not extended behind the 
mirror. 

(d!) If the lines do not meet in a point, go over the 
work and correct the errors. 



LIGHT 



193 



(0) Similarly locate the image I 2 of the point _Zi, 
and draw the head and tail of the reflected arrow at 
the points that are the images of the head and tail 
of the real arrow. Also join the head and tail by a 
straight line representing the shaft of the reflected 
arrow. If time permits, the middle point of the shaft 
should be located precisely as were the two extreme 
points, and it will be found to fall into a straight line 
with them. 

(/) Join tj and I x with i 2 and I v respectively, by 
straight lines intersecting MM' in points a and A. 
Measure accurately the distances I X A and I 2 A ; also 
measure the distances of i x and i 2 from a. 

(</) Measure the angles i x aM and i 2 aM, and com- 
pare their values. Do the same for I X AM and I 2 AM. 
Tabulate the results as follows : — 

Numerical Data 



Distances and Angles 


Differences 


Per Cent 
Errors 


i x a 


i 2 a 






I X A 


I 2 A 






ijaM 


i./iM 






I X A M 


I.,.\M 







For the per cent error of distance, find by what per 
cent i 2 a and I 2 A differ from i x a and I X A, respectively. 



194 LABORATORY EXERCISES IN PHYSICS 

For the per cent error of angle, find by what per cent 
each angle differs from 90 degrees. 

Sources of Error. — Small errors in placing the pins 
are greatly magnified in their effect on the position 
of the image point. The farther apart the pins are 
placed, the less are the errors magnified. 

Inferences. — (a) Are the per cent differences too 
large fairly to be ascribed to errors of experiment ? 

(5) State the location of the image (as to direction 
and distance from the mirror) compared with that of 
the object. 

(<?) Compare the object and image as to size. 

(c?) Describe the position of the image (erect, 
inverted, or laterally inverted). 

(0) As to character, is the image real or virtual ? 

Additional Work. — If the instructor desire, this method may 
be employed exactly as above, to locate and describe the image 
of an arrow in a concave or convex cylindrical mirror. 



Exercise Number 54 

refractive index 

References 

A 284-286 GP 303-313 J 42-51 

C 335-342 H 467-473 M & T 353-355 

C & C 256-261 H & W 300-306 W & H 381-385 
GE 232-237 

Purpose. — The refractive index of glass with 
reference to air is to be determined. 



LIGHT 



195 



Apparatus. — The apparatus needed consists of 
pins, dividers, draughtsman's triangle, rule, and a 
rectangular piece of plate-glass with two of its 
narrow parallel faces well polished. 

Operations. — (a) Across the middle of the note- 
book page, draw a line, ss', to indicate the common 
surface of the glass and air. Place the glass flat upon 
the page, and bring the edge of one of the polished 
narrow faces into 
exact coincidence /' 

with the line ss r . 
The plate may be 
fastened in this 
position by bits of 
beeswax. 

(J) Stick a pin at 
a point, a v against 
the edge opposite 
to ss f and near one 
corner of the plate. 
Place the eye oppo- 
site this pin and on 
the level of the page. Now look through the glass 
at the pin. Note the position of the eye at which 
the image of the pin seen through the glass coincides 
with the pin itself as seen above the glass. What is 
the direction of the line from the pin to the eye with 
reference to the surface, ss f ? 

(c) Move the eye toward one side, keeping the image 
of the pin in sight, and noting the change in the posi- 
tion of the image as referred to that of the pin itself. 




Fig. 41. — Illustrating the operations of 
Exercise 54. 



196 LABORATORY EXERCISES IN PHYSICS 

(c?) Stick a pin, a v against the glass, and in line 
with the eye and the image of the first pin. 

(0) Near the edge of the page stick a third pin, 
a 3 , so as to hide a 2 and the image of a v See that 
the pins are erect and accurately placed, and that the 
glass has not moved from its first position. 

(/) Now remove the glass ; and draw the line 
a x a v which is the path of the ray from a x through 
the glass to the point, # 2 , in the common surface, ss', 
of the glass and air. 

(#) Draw also a 2 a s , which is the path of the same 
ray through the air, after refraction at ss r . a x a 2 is 
the incident ray ; a 2 is the point of incidence and 
also of refraction ; and a 2 a z is the refracted ray. 

Qi) Through a 2 draw nn ! perpendicular to ss f . 
This is called the normal to the common surface (or 
interface) of the two media. 

(i) With a 2 as a centre, and as large a radius as 
practicable, describe a circumference cutting a x a 2 in 
point p, and a 2 a z in point p 1 . (^a x a 2 and a 2 a s are to 
be extended, if necessary.) From p and p f drop 
perpendiculars to nn\ cutting it in q and q f respec- 
tively. 

(y) Measure pq and p r q f as accurately as possible 

in millimeters. The quotient -^ is the index of 

refraction from glass to air, and this ratio inverted, 

i.e. L - L - (=ra), is the index of refraction from air 
pq 

to glass, or, in other words, the refractive index of 

glass referred to air. 



LIGHT 197 

(&) Repeat the operations as many times as the 
time will permit, using each time a different angle of 
incidence. Record values ofp'q\pq, and the refrac- 
tive index, m, in a tabular form of three columns. 
Note also whether the values of m are equal within 
the limits of experimental error, and record the mean 
value of m. 

Sources of Error. — (a) The edge of the glass may 
not exactly coincide with the line ss f . 

(6) Errors may arise from personal equation in 
setting the pins ; also in construction and measure- 
ment. The lines should be drawn as fine as possible 
with a sharp-pointed lead pencil. 

Lessons. — Refractive indices are very important 
in the calculations according to which the lenses and 
prisms used in all optical work are ground. Does 
refraction occur if the incident ray is perpendicular 
to the interface ? State two laws of refraction which 
are verified by your observations. 

If it = the radius of the circle, i the angle of incidence, and 
r the angle of refraction, 



n' r.' 



. . pq , . p'q 

sin i = ^ and sin r = -jy- m , 

Ix it 

whence the Index of Refraction (from glass to air), 

pq 
1 _ sin i _ R _ pq 
m sin r ])'(/ p'qf 

~7T 
In accurate measurements of indices of refraction flic angles 
themselves are read oil' on an accurately graduated circle fitted 
with a vernier and a magnifying glass, The instrument thus 
used is called a spectrometer. 



198 LABORATORY EXERCISES IN PHYSICS 

Additional Work. — If the student have time it will be profit- 
able to find by trial the approximate value of the critical angle, 
i.e. the angle of incidence that corresponds to the maximum 
(90°) angle of refraction, and to find the image of the pin 
which results from total reflection of the incident waves at the 
surface, ss F . 



Exercise Number 55 
focal length of a lens 

References 

A 290-293, 318-323 H 477-480, 513-522 

C 348-350, 352, 353, 355-359 H & W 310-319 

C & C 269-272, 295-304 J 60-67, 84-87 

GE 238-240, 270-275 M & T 350-352, 355, 360-367 

GP 315-320, 327, 389-391 W & H 386, 403-405, 416 

Purpose. — The purpose of this exercise is to deter- 
mine the principal focal distance of a convex lens, 
and to investigate the effect upon its focal length of 
combining with it, firstly, another convex lens, and, 
secondly, a concave lens. 

Apparatus. — A metric rule is mounted on a sup- 
port so that it can be turned about either a horizon- 
tal or a vertical axis. Three support blocks are fitted 
to the rule, as shown. The rule fits into the rec- 
tangular groove, its upper surface being flush with 
the upper face of the block, which is held in place by 
two stiff rubber bands. Wire nails are stuck upright 
into the block, and over them at top and bottom are 
stretched a pair of rubber bands, into which can be 
slipped a lens or a small cardboard screen. This 



LIGHT 



199 



arrangement allows the lens or screen to rest directly 
against the scale divisions of the rule. 




Fig. 42. — Rule and support blocks, mounted in a clamp so that they 
may be turned in any direction. 

Two double convex lenses, unmounted, and each 
having a focal length of from 10 to 20 cm., and a con- 
cave lens, are provided. 

Operations. — (jol) Slip the blocks, A and B, on to 
the rule. Place a double convex lens between the 
uprights of A and the screen between those of B. 

(J) See that the curtains are pulled about two- 
thirds of the way down so as partially to darken the 
room. 

(c) Point the rule toward the most distant bright 
object that is visible through one of the windows, 
and, having the lens toward the window and between 
the. latter and the screen, move the screen toward 
the lens or away from it until a perfectly distinct 
inverted image of the distant object appears upon 
the screen. 

(d) Read on the rule the positions of the lens and 
the screen, and by subtraction deduce the distance 



200 LABORATORY EXERCISES IN PHYSICS 

between them. Make at least three independent set- 
tings, changing the position of the lens on the rule 
each time. 

(<?) Place a second convex lens in front of the first 
and repeat the observations. 

(/) Replace the second convex lens by a concave 
lens and repeat the operations. The two lenses should 
not be more than two centimeters apart. 

Data. — Tabulate all of the readings. In each ob- 
servation the focal length is the difference between 
the lens reading and the screen reading. In each 
case, record the average of the differences as the 
mean focal length of the lens or of the combination. 
Record the letters which are marked on the lenses, so 
that they may be recognized when wanted again. 

Sources of Error. — From what sources may errors 
arise ? 

Inferences. — (a) In obtaining the principal focal 
distance, why should a distant object be chosen ? 
(With a long focus lens the object should be in- 
finitely distant, but with a lens of 10 or 20 cm. focal 
length, an object two or three hundred feet away will 
do.) (Why?) 

(J) What two optical instruments are represented 
by the single convex lens and screen thus combined? 

(<?) When a second convex lens is placed in front 
of the first, what is the effect upon the focal length 
of the first lens ? 

(d) What is the effect of a concave lens ? What 
kinds of cases of defective sight are corrected by 
applying the principles illustrated in (e) and (cZ) ? 



LIGHT 201 

Exercise Number 56 
conjugate foci of a convex lens 

References 

A 290-293, 318-323 H 477-484, 513-520 

C 350-359 H & W 309-319 

C & C 273-275, 295-304 J 68-80, 84-87 

GE 241-246, 270-275 M & T 360-375 

GP 315-327, 384-392 W & H 388-390, 410-416 

Purpose. — The purpose of this exercise is (a) to 
investigate the conditions in accordance with which 
images are formed by a double convex lens, and 
(6) to verify the law of conjugate foci. 

Apparatus. — The convex lens, rule, and blocks of 
Exercise 55 may be used, or, if preferred, the blocks 
of Exercises 49 and 51. In the latter case the rule 
should be fastened by brads to a smooth board, whose 
ends may be supported by blocks, at the proper height 
above the table. The lens and screen are to be 
mounted at the centres of the blocks just as in Ex- 
ercise 55. The box suggested in Exercise 49 may 
easily be adapted to enclose either apparatus, and, 
if available, should be used. The rule and sliding 
supports as used in this and the preceding exercises 
constitute a very simple optical bench. A source of 
light is also provided, and may be a candle, small 
lamp, gas jet, or an incandescent electric Lamp. It 
should be enclosed by a suitable opaque chimney or 
tube,* perforated by a circular aperture about 2 cm. 

•Fig. 43, page 200. 



202 LABORATORY EXERCISES IN PHYSICS 

in diameter at the height of the centre of the light. 
A pin is fastened (by solder or wax) so that its head 
projects into the aperture from below, and is an 
object of which a distinct image may conveniently be 
obtained. 

Part A. Relations of Image to Object 

Operations. — (a) The focal distance of the lens 
is known from the preceding exercise, or may be 
given by the instructor. Support the optical bench 
so that it is horizontal and the centre of lens and 
screen in line with the centre of the light and of the 
circular aperture, the aperture being exactly at the 
end of the rule. Place the lens at a distance, jo, 
greater than twice focal distance from the aperture 
Qp > 2/), slide the screen up close to the lens, and, 
moving the screen slowly away, watch for the image 
to appear upon it. When the image appears, move 
the screen gradually backward or forward until the 
image of the pin is as distinct as possible. (Another 
lens may be used as a magnifying glass for examining 
the image, if desired.) 

(J) Examine the image. Is it real or virtual ? 
Erect or inverted ? Magnified or diminished ? Is 
it located at a distance, p\ > If (greater than twice 
focal distance), p f < 2f, or p f = 2f? Tabulate these 
observations under the headings Character, Size, 
Position, and Location. 

(<?) Make the distance between lens and object 
equal to twice focal distance Qp = 2/), and repeat 
operations and observations. 



LIGHT 203 

(d) Kepeat with] the lens nearer (p < 2/). 

(e) Make p—f^ Look through the lens at the 
object. Observe that light comes from it, but no 
image appears. The rays from each point of the 
source are now nearly parallel. 

(jO Make J><f, and look through the lens 
toward the object. Tabulate observations as before. 

Applications. — Optical Instruments. — (a) Which of 
the cases represents the eye, or the camera? 

(b) Which represents the projecting lantern, or 
the camera when used for enlarging ? 

(c) Which case represents the magnifying glass ? 

(d) Which the "spot light" used on the stage? 

(e) In cases (a) and (d) the screen may be re- 
moved and the image viewed from a point near the 
end of the bench that is opposite the object. A 
convex lens, placed at its focal distance from wheri 
tic screen was, will act as a magnifier to increase the 
apparent size and distinctness of the object. The 
paths of the light waves are parallelized by the sec- 
ond lens, and are converged at points on the retina 
by the crystalline lens of the eye. In which of the 
two cases just indicated, do the two lenses represent 
the objective and eye piece of the refracting tele- 
scope ? The objective and eyepiece of the com- 
pound microscope I 

OPTIONAL PROBLEM 

Image Size and Distance. — Measure in cm. the distances 
of object and of image from lens, also their lengths. Express 

decimally the ratio of image distance to object distance, and 

the ratio of linear size of image to that of object. Tabulate 



204 LABORATORY EXERCISES IN PHYSICS 

all the data for a number of different trials. State the relation 
of linear size of image to linear size of object in terms of their 
corresponding distances from the screen. 

Part B. Conjugate Focal Distances 

Repeat the operations of cases (a) and (5), Part A, 
and each time read on the rule the values of the dis- 
tances of object and image from the lens. These we 
have called p and p ! respectively. Make at least two 
settings for each of the two cases. In one trial place 
the screen at the end of the rule and move the lens 
till a distinct image appears on the screen, recording 
the values of p and p r as before. Now interchange 
the object and screen without disturbing the lens; 
observe, and state whether or not a distinct image is 
formed. Record these new values of p and^/. 

Data. — For each setting, take the reciprocals of p 

and p\ expressing them decimally. Add - and — 
for each observation. Also find the value of — . 

/ 

Tabulate the values of p. p f . -, and —.\ and also — | — T 
I 1 1 p p' p p' 

and — , placing each set of values in a vertical col- 
umn, under its appropriate letter, corresponding val- 
ues opposite one another. 

Sources of Error. — State briefly the sources from 
which errors may arise. 

Inference. — (<x) Experimental errors aside, are the 

sums, - H — 7, equal to one another ? 
p p r ^ 



LIGHT 205 

(5) Find their average. Does it differ from — ? 

(e) By what per cent ? * 

(cT) If this per cent is small enough to be ascribed 
to experimental errors, express the law by a general 
formula. 

(e) State the law in words, p and p' are called 
the conjugate focal distances, and / the principal 
focal distance. 

Exercise Number 57 
study of spectra 

References 

A 295-300, 304-309, 318-323 H 486, 487, 500-506 

C 346, 360 H & AV 320, 321 

C & C 277-286 J 91-99 

GE 249-259 M & T 387-395 

GP 315, 329-342 W & H 392-394, 397-402 

Purpose. — In this exercise, the purpose is to in- 
vestigate the composition of light emitted from dif- 
ferent sources. 

Apparatus. — In addition to the source of light and 
perforated chimney, Fig. 43, p. 206, a prism and a 
Bunsen burner are provided. The perforation in 
the chimney is covered with a plate, having in it a 
narrow horizontal slit. 

Operations and Observations. — (a) Cut out a strip 
of white unglazed paper, about half a cent [meter wide 
and three centimeters long. Fasten it to a piece of 
black cloth or to a black photographic card-mount, 



206 LABORATORY EXERCISES IN PHYSICS 




and place it in strong light from the sun or sky. 
Stand so that the eye is about a meter 
from it, and look directly at it. 

(6) Now hold the prism in front 
of the eyes with its lower face about 
parallel to the line of sight, and its 
edges parallel to the length of the 
white strip. The strip will disap- 
pear ; but if now the prism be raised 
a little without rotating, a beauti- 
fully colored image (spectrum) of 
the strip will be seen through the 
prism, apparently above where the 
strip is. 

(<?) Without otherwise changing 
the position of the prism, rotate it 
a little, first one way and then the 
other, about -its axis, until the colors 
show with the greatest distinctness 
and brilliancy. This will occur at 
or they may be the angle of minimum deviation ; that 
pushed in from the \^ at the angle at which the light, 

sides, making aver- . , ^ . „ _ 

tical slit. incident on the prism trom the strip, 



i 



LJ 

Fig. 43. — Chim- 
ney of wood and 
sheet iron for Exer- 
cises 56 and 57. The 
plates may he re- 
moved, leaving the 
circular aperture ; 




Fig. 44. — Showing position of the strip and its colored image, and 
the real and apparent paths of the rays. 



LIGHT 207 

is least turned from its original path. This position 
corresponds also, of course, to the minimum displace- 
ment of the image. 

(d) Carefully examine the colors ; and make a 
sketch of the spectrum, writing down the names of 
the colors in their order. 

(e) Make a diagram of the arrangement, tracing 
the approximate direction which the light waves 
actually take in travelling from the strip to the eye, 
and also the directions which apparently they take in 
coming from the image. 

(/) Which waves are deviated the least, those 
which cause the sensation of red, or those which 
cause the sensation of violet ? Number the colors 
on the spectrum sketch in order, from the least de- 
viated to the most deviated. What is the original 
source, and also the immediate source, of the waves 
which are thus separated ? Why are their directions 
changed, some more than others ? 

(^/) Place a second prism between the first prism 
and the eyes, the second being inverted as shown in 
Fig. 45. What is the effect ? Are the waves recom- 
bined ? What is " white 
light " ? 

(K) Now place the lamp 
inside the chimney, the light 
opposite the horizontal slit 
and close to it, the room hav- 
ing been darkened. Find 

and examine the spectrum of the light coming 
through the slit, comparing it with that previously 




208 LABORATORY EXERCISES IN PHYSICS 

given by reflection from the strip of paper. This is 
the spectrum from white-hot carbon. A stick with 
a spark on the end of it, or the filament of an incan- 
descent electric lamp without the slit, will give the 
same result. 

(i) Replace the lamp by the Bunsen burner, and 
after making sure that the part of the flame opposite 
the slit is colorless, let another student hold in the 
flame below the slit a platinum wire loop which has 
been moistened with distilled water and dipped into 
common salt or baking soda. Examine the spectrum, 
which is due to sodium vapor. What color appears 
most prominently ? 

(j) In like manner examine the spectra given by 
incandescent vapors of two or three other metals. 
The chemically pure bromides or chlorides of any of 
the following metals may be provided: potassium, 
calcium, strontium, and barium. Compare the colors 
and their relative positions. Does each metal have 
its own set of colors ? Do they have the same posi- 
tions as the corresponding colors in the solar or the 
carbon spectra ? 

Caution. — There should be a separate labelled 
platinum loop for each salt, and the greatest care 
should be exercised in order not to mix the salts ; 
else the spectrum of the metal under examination 
will contain the colors of some other metals. It is 
extremely difficult to exclude the sodium band, be- 
cause sodium is everywhere in the dust of the room. 
The sodium band will flash out whenever anything is 
dusted near the flame. Try it. 



LIGHT 209 

Lessons. — With suitably delicate apparatus (spectroscope), 
may the vapor spectra of some metals be used for detecting with 
certainty the presence of these metals in compounds ? In the 
spectroscope a combination of lenses is used in order to make 
the light pass in a parallel beam from the slit to the prism, 
and to make the refracted images of the slit more distinct. 
Each colored image of the slit then appears as a fairly distinct 
band, and in a position which is perfectly definite for a given 
prism and for that particular wave length of light. The lack 
of distinctness of the bands in the case of the prism, w T hen used 
without the lenses, is due to the overlapping of the images of 
the slit when radiations of different wave lengths are present. 

If time is given for additional work, try the effect of viewing 
the carbon spectrum or the solar spectrum through pieces of 
colored glass, and state in your notes which colors are absorbed 
and which are transmitted by glass of each color examined. 

Read the sections on spectrum analysis in the reference books 
to which you have access. 



CHAPTER VII 
APPENDICES 

A. ERRORS AND SIGNIFICANT FIGURES 

1. Errors. — Different measurements of the same quantity, 
even when made with the same care, are found to differ from 
one another, — the differences becoming less and less as the 
observer becomes more skillful, or as the accuracy of the in- 
struments is increased. These differences are due to experi- 
mental errors, as distinguished from mistakes or blunders in 
either observation or calculation. 

Experimental errors are called errors of observation when 
they result from variations in the judgment or perceptions 
of the observer, and instrumental errors when they result from 
imperfections of the instruments or apparatus employed. 

Instrumental errors may often be determined, and a correc- 
tion applied for each of them so as to eliminate their effects 
from the result. 

The error of a single observation is the amount by which it 
differs from the result accepted by theory as the true one. The 
mathematical theory of probabilities shows that if a series of 
measurements has been made of the same quantity under the 
same conditions and with the same care, the mean or average 
of this series has much greater probability than any single 
observation, i.e. it is much more likely to be near the true 
value. 

2. Mean of a Series. — The probability of the mean of four 
observations is twice that of a single one; of nine, three times; 
of sixteen, four times, and so on, i.e., the probability of the 
mean i< proportional to the square root of the number of ob- 
servations. Besides increasing the probability of the mean. 
the taking of a series of observations make- it easier to detect 
blunders. 

3. Significant Figures. The magnitude of a physical 
quantity should he stated jusl as accurately as it has been 

211 



212 APPENDICES 

measured by the observer, no more, no less. For example, 
if the mean or average of a set of measurements of a given line, 
made with a metric rule, comes out 0.0204639 meters, the 2 
nearest the left is the first significant figure. The two zeros 
at the left of this 2 are not significant figures, since they serve 
merely to locate the decimal point; but the zero after the 2 is 
significant, for.it shows that the number of thousandths of a 
meter is more than twenty and less than twenty-one. Again, 
since the 4 represents four-tenths of the smallest division of the 
metric rule, it was obtained in the observations by estimating 
tenths of a division with the eye, and it is therefore in doubt 
because an error of at least one-tenth of a division is probable 
even in the judgment of a practiced observer. Thus we are 
not sure that the third significant figure of the true value may 
not be 3 or 5 instead of 4; and so it must be apparent that all 
figures in the fourth and subsequent significant places are 
wholly unknown to us. Since they have no significance, they 
should be rejected from the statement of the result. When 
discarding these figures, however, we should write 5 instead of 4 
for the last or third significant figure, because 4.6 is nearer to 
5 than it is to 4. 

4. Rules for Precision of Numerical Statement. — In 
order that the numerical data may show correctly the degree of 
accuracy attained, as well as to save unnecessary labor in the 
calculations, the student should adopt and hold to the follow- 
ing rules in the reduction of his results. 

1. In every statement of an observation, sum, difference, 
or average, retain the first doubtful figure, and reject all that 
follow it. If the first figure discarded is greater than 5, in- 
crease by one the last figure retained. If the figure in the last 
place to be retained in accordance with the rule is a zero, retain 
such zero. Example, — write 25.20 cm. instead of 25.2 in a 
case where the quantity is measured to hundredths of a centi- 
meter, and found to be nearer to twenty-five and twenty hun- 
dredths than to twenty-five and nineteen hundredths or twenty- 
five and twenty one hundredths. 

2. In products, quotients, and partial products, retain only 
as many significant figures, counting from the first at the left, 
as there are in the measured factor having the least number of 
significant places in accordance with Rule 1. 



APPENDICES 213 

B. METHODS OF MEASURING LENGTHS 
1. Use of a Rule. — Place the rule on edge so as to bring 
the division marks into contact with the line to be measured. 
In reading or setting the rule at any point stand directly in 
front of the point and sight downward at it along the divi- 
sion lines of the rule, thus avoiding the error of parallax. If 
the line is longer than the rule, mark the position of the end 
of the rule by a straight edged bit of paper and measure again 
from the mark. On a long line measure to the nearest milli- 
meter. In measuring a line less than 10 cm. long estimate in 
tenths any remainder less than a millimeter thus: if the re- 
mainder is just perceptible call it 0.1 mm., if just perceptibly 
less or more than a quarter millimeter call it 0.2 or 0.3 and so on. 
If the result is to be expressed in meters and it is (say) 2 m.-f- 
25 cm. -f 9 mm. + 0.6 mm., write it 2.2596 m. If it is to be 
expressed in centimeters, write it 225.96 cm., i.e., always ex- 
press the result as a certain number of units and a decimal 
fraction thereof. If very accurate measurements are to be 
made with a rule, it is better not to use the end divisions, as 
the rule may be slightly worn at the ends. If the end divisions 
are rejected do not forget to take account of it in adding up 
the units of length for the final result. In measuring a quantity, 
a series of measurements is usually taken; and the individual 
measurements and their mean should be tabulated. (Cf. Ap- 
pendix A Art. 2.) 

2. Use of Squared 

Blocks. — Fig. 46 shows a 
method of measuring the 
diameter of a round body. 
The inner planes oi the 
blocks, being tangent 
planes, are perpendicular 
to the ends of the diameter. 
Therefore when the rule is 




Fig. 46. 



placed as Bhown, the part of it included between these planes 
is parallel to the diameter and hence equal to it (parallel lines 
included between parallel planes are equal . Sigh! along 
the scale divisions to avoid parallax. 

or Calipers. By tapping lightly on the inner or 
the outer edge of "ii<- !,•«: of the calipers, separate the tip- or 



214 APPENDICES 

bring them together, so that they just touch opposite ends of 
the diameter to be measured. With very little practice one 
can feel if the tips are too tight or too loose on the opposite 
surfaces of the body that he is measuring. Apply the calipers 
to the rule so that the inner face of one tip just splits a division 
line of the rule, then read the position of the inner face of the 
other tip to tenths of the smallest division. Avoid parallax. 
The difference between the readings is the length to be deter- 
mined. 

4. Use of the Vernier Slide Caliper. — (a) Loosen the 
set screw, s (Fig 47); and, grasping the scale in the right hand, 

press the thumb against 
the little projection, p, 




■■■SI ^■■■■i..fiL.i l ,.!L„i,.,7i l .Mi.. l ?i.M,i1 below the vernier till the 

movable jaw withdraws 



from the fixed one. Now 
place the body between 
the jaws; and, with the 
Fig. 47.— Vernier Slide Caliper. thumb on the projection, 

press the jaws together against the two surfaces at the extrem- 
ities of the diameter that is to be measured, so that they are 
just in contact with these surfaces. 

(b) By means of the set screw, fasten the movable jaw in 
position, remove the cylinder, and take the reading of the 
caliper in accordance with the rule that follows. 

Read and record the number of centimeters and whole milli- 
meters from the zero of the scale to the zero of the vernier; and 
add the number of tenths of a millimeter in the remainder. This 
is denoted by the number of the line on the vernier which most nearly 
coincides with some line on the scale: e.g. if line number 3 on 
the vernier coincides with some line on the scale, the remainder 
is .3 mm. Avoid parallax. 

In order to understand why this is so, notice that the vernier 
scale is 9 mm. long and is divided into 10 equal parts; hence, 
each vernier division is .9 mm. long. On the other hand each 
division of the fixed scale is 1.0 mm. long. Therefore when 
vernier line 3 coincides with some fixed scale line, vernier line 
2 falls .1 mm. short of the fixed scale line next to the left of it. 
It is obvious also that vernier line 1 must fall .2 mm. short of 
the fixed scale line next to the left of it. Finally the vernier 



APPEXDICES 



215 



line must fall .3 mm. short of the fixed scale line next to the 
left of it. But this space of .3 mm. is the fractional part of a 
millimeter that was to be measured. 

Xote that the first line on the vernier is zero. 

In some verniers 20 divisions of the vernier = 19 of the 
fixed scale, in others 25 of the vernier = 24 of the scale and 
so on. The principle is precisely the same. 

If the student has difficulty in understanding the principle 
of the vernier, let him practice reading and reasoning as above, 
using a large model scale and vernier which he can easily make 
of wood or of cardboard, the fixed scale divisions being each 
1 cm. long and the vernier scale divisions being each .9 cm. 
(9 mm.) long. 

5. Use of the Micrometer Screw Caliper. — In one 
kind of micrometer caliper, the pitch of the screw (distance 
between two adjacent threads, measured parallel to the axis) 
is 1 mm.; and the circumference of the head is divided by a 

circular scale into one hundred 

U||* equal parts. In another kind, 
^L-^-H- f I P f (Fig. 48), the pitch is J mm.; and 

the circular scale has fifty equal 
parts. When the end of the 
screw rests against the stop, B 
(without strain), the edge of the 

£l G u 4 ?~~ Micr ? met ? r £ ali P er circular scale should coincide 
Pitch \ mm. ( ircular Scale in ... . 

50 equal parts. with the zero mark of the linear 

scale, a; and the zero line of the circular scale should exactly 

coincide with the horizontal reference line. 

It Bhould be noticed that in the first kind of micrometer 
caliper, the zero mark of the circular scale is identical with the 
1.00 mark; and in the second kind it is identical with the .50 
mark. 

In the first kind of micrometer caliper, it' the head of the 
screw ifl given one complete turn toward you. the M-rew end' 

retires from the Mop to a distance equal to the pitch o! the 
screw (\ mm.); and the edge of the circular Male will coincide 
with the division l on the linear scale, which therefore den 
the distance in millimeters between the Bcrew and the stop. 

AIm). the zero mark of the circular scale will again coincide 
with the reference mark. Now if the head be turned farther 





216 APPENDICES 

around till the division numbered 25 coincides with the reference 
line, the screw has retired from the stop a further distance 
equal to twenty-five hundredths of the pitch of the screw {i.e. 
.25 mm.). Similarly, if the screw has been turned so that the 
linear scale shows seven and a fraction of its millimeter spaces, 
and the 69th division of the circular scale coincides with the 
reference line, it is clear that the screw has turned through 
seven and sixty-nine hundredths revolutions, and the screw end 
is distant from the stop just 7.69 mm. 

6. To Measure the Diameter of a Wire. — (a) Withdraw 
the screw from the stop and place a straight portion of the wire 
between them, so that it lies -fiat against the face of the stop. 
Turn the head till the face of the screw end rests against the 
wire firmly enough so that you can just feel the resistance. 

(b) To read the First Kind of Caliper. — With the line of sight 
perpendicular to the scales at the reference line, read the num- 
ber of whole millimeters on the linear scale, and the number 
of tenths and hundredths of millimeters on the circular scale. 

(c) Determine the zero error by setting the screw end gently 
against the stop, and observing the scale readings as before. 
If the zero of the circular scale coincides with the reference 
line, no correction is required. If there is a small negative 
reading, it must be added to all readings of the caliper; and if 
there is a small positive reading, it must be subtracted. (Why?) 

(d) To read the Second Kind of Caliper. — In this case also, 
each division of the circular scale corresponds to one-hundredth 
of a millimeter (because ^ of § mm. = jj mm.). Read the 
number of whole millimeters on the linear scale, and add the 
hundredths indicated on the circular scale just as directed 
above; but if the fractional part of a millimeter exposed on the 
linear scale is greater than one-half, then .50 must be added to 
the reading, in order to state correctly the fractional part. 
(Why?) 

Thus, in Fig. 48, the caliper reads 4.50 mm. If D were 
turned so as to bring C nearer to B by g 5 of a revolution, the 
reading would be 4.45 mm.; but if D were turned so as to with- 
draw C by f§ of a revolution, the corresponding reading would 
be 4.23+ .50 =4.73 mm. 

(e) Several measurements should always be taken along 
different parts of the sample of wire. (Why?) 



APPENDICES 



217 



(/) Micrometers measuring in inches usually have a linear 
scale with units ^~ of an inch in length, and the circular scale 
divided into 40 equal parts. What fraction of an inch does 
one division of the circular scale measure? 

(g) If the head of the screw is fairly large, it is easy to esti- 
mate tenths of the divisions of the circular scale and thus 
estimate thousandths of millimeters, or ten-thousandths of 
inches. 

C. METHODS OF DETERMINING AREAS AND 
VOLUMES 

1. Plane and Solid Geometrical Figures. — The areas 
of plane polygons and of surfaces of geometrical solids and the 
volumes of such solids may be obtained by calculation accord- 
ing to the rules of plane and solid geometry. The student 
should refer to his geometry for these rules whenever he finds 
it necessary to refresh his memory. The dimensions from 
which the areas or volumes are computed should each be the 
mean of a series of measurements, the smallest dimension 
being measured with the greatest care. Cf. Appendix A, Art. 
2-4; also Appendix B. 

2. Measuring Volume with a Graduate. — Compare the 
divisions on the graduate with the numbers, to learn how 
many cm. 3 (cubic centimeters) each division represents. 

Thus if , as in Fig. 49, th?re are 5 'spaces 
between the GO and the SO mark, then 5 di- 
visions represent 20 cm. 3 ; hence 1 division 
, ^v =4 cm. 3 , and each tenth of a division = 
"^ 0.4 cm. 3 The single divisions of a graduate 

having 100 cm. 3 capacity usually represent 
single cubic centimeters, and those of a 250 
cm. 3 graduate represent 2 cm. 3 each. What 
would 0.1 of one of these di\ isions repre- 



l-^3 



Fig. 49.- Showing 
the posit ion of the eye sent? 

when taking a read- To measure a liquid in such a graduate 

in s- hold it at it- npper end between the! humb 

and forefinger, allowing it to swing freely till it settles with 

Itfl axis vertical. Then read on the BCale the position <A the 

middle line of the meniscufl *>'.'.. tin- saucer-shaped surfa 
Keep the eye on a level with the divisions a- in Fig. 19. If 



218 



APPENDICES 



the position of the eye is correct the divisions will look straight 
instead of curved. Estimate the tenths of a division. 

To measure a Solid, fill the graduate with water to any con- 
venient division mark and take the reading as directed in the 
preceding paragraph. Incline the graduate and let the solid 
slide gently to the bottom, so as to avoid breaking the 
glass or splashing the water, and take the new reading. Ob- 
viously, the difference between the two readings is the volume 
of water displaced by the solid, and hence it is equal to the 
volume of the solid. Take the mean of several such deter- 
minations, using a different quantity of water, and set down 
all the data in a neat tabular form. If the readings are taken 
from the bottom of the meniscus both times the subtraction 
eliminates the error of assuming that to be the position the 
surface would have if plane; anil since it is easier to read accur- 
ately from the bottom than from the middle the student is 
advised to do so. 

D. METHODS OF MEASURING MASS 

1. The Equal Arm Balance. Operations.— (a) See that 
the balance and the weights are free from dust. 

(6) See that all the weights are present. To ascertain this 
easily, notice whether the sockets in which the larger weights 
belong are all filled; then see that all of the smaller weights are 
in order in a tray provided for the purpose and placed near 
the centre of the table, so that they will not be dropped upon 
the floor. The fractional denominations in most students' 
sets are as follows: decigrams, 5, 2, 1, 1; centigrams, 5, 2, 2, 1. 
Report immediately if the set is incomplete or if the balance is 
not in perfect condition. 

(c) Adjust the balance to equilibrium by adding fine sand 
to the lighter pan till the pointer swings to equal distances 
on opposite sides of the zero position. If too much should be 
added, remove some. 

(d) Place the object near the centre of one pan and the 
weights on the other, the largest in the centre and the others 
close around it. The weights should be tried in order, begin- 
ning with one known to be large enough. If the last weight be 
too great, replace it by the next smaller; if too small, add the 
next smaller. In this manner, continue with the systematic 



APPENDICES 



219 



trial of the weights until the opposite excursions of the 
pointer are equal. 

(e) Add up the weights in the pan. Their sum is equal to 
the mass of the object. 

(/) Add up the weights 
remaining and add their 
sum to the sum of those in 
the pan. Obviously, if the 
result is the total number 
of grams in • the set, it is 
known that no mistake has 
been made in the count, and 
that no pieces have been 
lost. 

(g) Remove the object to 
the other pan and weigh as 
before. Take the mean of 
the two weights thus ob- 
tained and record it as the 
mass of the object. 

(h) When done with the 
weighing, see that both 
scales and weights are in 
perfect order, return the 
weights and pincers to their 
proper places. These direc- 
tions are to be followed in all Fig. 50. — Showing a convenient method 
weighings unless it be other- of supporting a "German hand balance." 
wise ordered. 

Precautions. — (a) The weights and scales must be kept 
free from dust and liquids. 

(6) The weights must be handled with pincers only. 

(c) The balances should not be permitted to vibrate while 
object or weights are being placed in the pans. 

These directions apply to balances that have no adjusting 
screw and no beam and pan arrests. If the h<il<i>i<<s are 
provided with lx run and pan arrests, the lexers that work these 
should be lifted each time before adding or removing object 
or weights, so as to prevent swinging during these operations. 
If there are no arrests, the pan may be held m t lie hand while 




220 APPENDICES 

the load is being changed. // there is a screw for adjusting to 
equilibrium, this is turned toward the lighter side, instead of 
adding sand. Hand balances may be conveniently suspended 
upon a vertical support rod by means of a screw clamp as in 
Fig. 50. The pans should not be far above the surface of the 
table. 




Fig. 51.— The Trip Scales. 

2. The Trip Scales. Operation. — (a) Place the slider 
at zero. (Fig. 51.) 

(b) See that the ends of the knife-edge do not rub against 
the ends of the bearings. If they do so, the beam will not 
oscillate freely, but will come to rest rather suddenly. Move 
the beam very slightly forward or backward till there is no 
friction. 

(c) In front of the pointer are two little nuts. Turn the 
right-hand nut toward you, so that the two nuts are unlocked; 
then turn both nuts toward the lighter pan till the balance is 
adjusted. Lock the nuts in place by turning them toward 
each other. 

(d) Weigh as with the equal-arm balance to within 5 grams; 
then move the sliding weight along the graduated beam till 
equilibrium results, and read on the scale the position of the 
left edge of the slider. 

(e) The scale reads grams and tenths up to 5 grams; this 
reading is to be added to the sum of the weights if they are on 
the right-hand pan, and subtracted if they are on the left. 
(Why?) 

3. The Jolly Balance. — If one has calibrated a spring as 
in Exercise 7, he knows just the amount by which each gm. 



APPENDICES 221 

elongates it. Therefore, if he wishes to weigh with it, all he 
needs to do is to take a reading of the pointer on the scale when 
there is no load on the pan, and then another when the object 
to be weighed is in the pan. The number of gms. that one 
scale division represents multiplied by the difference between 
the two scale readings is the mass of the body in gms. A 
spring mounted on a suitable adjustable support (like Fig. 4, 
but with more refined adjustments) is called a Jolly balance. 
If such a balance is to be used for hydrostatic weighing, as 
for Exercise 22, it usually has a second pan suspended below 
the first by a fine wire, and a movable shelf holding a vessel 
of water is placed at such a position that the lower pan will 
be submerged during each of the weighings. Then if r is the 
reading with no load, r x that with the body on the upper pan, 
and r 2 that with it on the lower pan, the density of the body 

is numerically D = — -, 

r l~ r 2 

for r x — r represents the weight of the body, and r t — r 2 repre- 
sents the buoyant force of the water on it. 

If the simple apparatus of Fig. 4 is to be used in this way 
the vessel of water may be supported on a thin board placed on 
a large retort ring below the second clamp, c'. 

If used for getting the density of a liquid (Exercise 22. Fart 
B), the suspended solid takes the place of the lower pan, and 
if rj, r 2 , and r 3 are respectively the reading with the dry solid 
in air, that with it submerged in water, and that with it sub- 
merged in the liquid, the density of the liquid is 

D=-^^> Why? 

The same principles apply if the Jolly balance is used for 
Exercises 20 or 21, or for measuring any forces whatever, since 
any elongation (difference between two readings) multiplied 
by the force that produces an elongation of 1 scale division 
equals the amount of force that produces the observed elonga- 
tion. 

4. A Iim n Kit Band Dynamometer, may be used on the 

same principle as the Jolly balance lor measuring forces in any 
direction, and is an excellent substitute for B spring balance for 

schools where funds for equipment are limited. 



222 



APPENDICES 



E. BAROMETER 
Reading the Barometer. — (a) Turn the screw (Fig. 52) 
to the left until the mercury in the cistern is seen to withdraw 
below the little ivory point at B. This ivory point represents 
the zero end of the scale that is attached to the metal case. 

(b) Looking so that the line of sight is tangent to the mer- 
cury in the cistern, slowly turn the screw to the right until 
the ivory point just meets its image reflected in the mercury. 

(c) By turning the screw D from you, raise the lower edge 
of the sliding (or vernier) scale, C, until you can see over the 
upper surface of the mercury column. 

(d) Place the eye on a level with the highest point of the 
mercury column, and by reversing the screw D lower the vernier 
till its zero line appears just tangent to the curved surface of 
the mercury. 

(e) Read the scale and vernier precisely as di- 
rected for the vernier slide caliper, Appendix B, 
Art. 4. 

(/) If the barometer reading is to be taken in 
inches instead of in centimeters, note that inches 
and tenths are measured by the fixed scale and 
hundredths of inches by the vernier. 

Correction for Temperature. — The temper, 
ature of the room being higher than 0° C, the 
mercury column and the scale by which it is 
I D measured are both expanded by the heat, and 
therefore are longer than they would be at 0°. 
As the readings of air pressure are customarily 
based upon the supposition that the temperature 
of the mercury is zero, it is usual to observe the 
; temperature of the barometer by means of the 
" attached thermometer" (E, Fig. 52), and to cor- 
rect the observed height of the column for the 
. error due to expansion. The correction is the dif- 
Weather Bureau ference between the expansion of the mercury col- 
Standard Sta- umn and that of the brass scale by which it is 
tion Barometer, measured. (Would a correction be necessary if 
both expanded equally?) Since the temperature of the room 
is above zero, and since the mercury expands more than does 
the brass, the observed height is too great, and the correction 



APPENDICES 223 

is to be subtracted. The amount of the correction is jointly 
proportional to the length and to the temperature of the 
mercury column . 

The corrections for all pressures and temperatures have been 
calculated, and are published in the tables of the United States 
Weather Bureau. Unfortunately, the pressures are expressed 
in inches and the temperature in Fahrenheit degrees. So that 
the barometer should be read accordingly, if its indication is 
to be thus corrected. 

To Find the Correction for Temperature, consult the 
Table for Reduction to 32° F., in accordance with the rule given 
below. 

In the vertical column at the left find the temperature that 
was observed on the attached thermometer. Follow the line 
of this number to the right till you reach a column of figures, 
headed by the pressure-reading that you observed. In this 
vertical column, the number directly opposite your attached 
thermometer-reading is the correction required. If the exact 
temperature and pressure that you observed are not shown in 
the table, select the nearest values that are tabulated. 

Other Corrections. — When readings simultaneous at 
different places are to be compared, they are all reduced to 
what they would be at sea level. The capillary depression of 
the mercury in the tube is corrected by permanently lowering 
the scale. 

F. SUGGESTIONS CONCERNING APPARATUS 

1. Exercises 1 and 2. This apparatus is easily "homemade. 

Length 150 to 200 cm., width 6 cm., thickness 2 cm. The 
weights may be cast from lead in a plaster of Paris mold. I [oles 
are drilled in them and in the wooden rod; and they arc fa 
tened by wire nails fitting snugly in these holes. Halls of 
any size with hooks maybe had from apparatus dealers. The 
ball must be heavy enough to hold t he pendulum in equilibrium 
as Bhown. 

2. Ex 5. If so ordered the dealers will furnish the ears with 
hooks both behind and in front. The Author uses strips of 

plate glass to run the cars on. They may be had from whole- 
sale glass dealers. They arc remnants and arc inexpensive 
(about 86c each). Mr. J. E. Crabbe of ( Cleveland uses very 



224 APPENDMJES 

successfully the rubber from an old golf ball instead of 
rubber tubing. With mass of car and load equal to 1,000 gm. 
or more, the masses may easily be adjusted to equality within 
20 gm. or 2 per cent. 

3. Ex. 7. Slotted weights for this Exercise and several 
others are easily cut with tinner's snips from sheet lead. 
The platform on which to suspend them may consist of a small 
square of thin board with a long stiff wire hook stuck into it 
perpendicularly at its center. The platform may be loaded 
with enough lead to give it the same mass as one of the slotted 
weights. Pans to hold ordinary weights may be made by 
soldering a wire bale on to a small pie pan. The weight of the 
pan may be adjusted as desired with drops of melted solder. 
These pans and weights are used in several other Exercises. 

4. Ex. 9. Expensive pulleys are not necessary, but if 
cheap ones from the hardware store are used, the weights used 
with them should be as heavy as possible. For large weights, 
" blank" bridge nuts may be bought at wholesale hardware 
dealers'. They are very cheap, are of various sizes, and those 
of a given size are so nearly of uniform weight that they may 
be adjusted to equality with a coarse file. (For platform sup- 
port see Art. 3 above.) 

5. Ex. 10. Plumber's safety chain may be bought by the 
pound of wholesale hardware dealers, and key rings by the 
dozen. Spring balances of all kinds are sold by Fairbanks, 
Morse & Co. (Chicago or Cleveland). The apparatus dealers 
sell a kind that have flat backs. These are the best for the 
purpose. The clamp hooks may be made from the drawing 
by any blacksmith. 

6. Ex. 11. The Author uses for inclined planes, boards 
about 6 ft. x 6 in. x -J in., as shown in Fig. 7. Narrow strips 
are nailed on the sides to keep the cars from running off. The 
same glass strips and cars (cf. Art. 2 above) as are used in 
Ex. 5 are used here. If the teacher prefers to use a pulley 
and weights instead of a spring balance, it may be set into a 
slot just above the upper end of the glass strip. (For pans and 
weights see Art. 3 above.) 

7. Ex. 12. The post, strut and back-board for this exercise 
may be made by any one who can use a saw and a plane, and 
drive a nail. The upright that supports the cross bar of the 



APPENDICES 225 

table may be used for the post; and the back-board may be 
clamped to it with a carpenter's hand screw. The tie may be 
attached to a screw eye in the upright. 

8. Ex. 13. [Exercises 13, 14, 15, and 17 are all on moments. 
It is not expected that all of these be required of every stu- 
dent.] The wire clevis may be made of Xo. 16 German sil- 
ver wire with a pair of square and a pair of round pliers. The 
holes in the meter stick should be smoothly drilled. Apparatus 
dealers sell clevises which slip over the bar, and with these the 
holes will be unnecessary. (For pans and weights see Art. 3 
above.) For measuring vertical upward forces an equal arm 
balance may be used. Attach a cord to one pan, and measure 
the pull on this cord by weights on the other pan. This device 
is more accurate than a spring balance or a pulley. 

9. Ex. 15. This exercise is useful in combating the too 
common assumption by students that every force is a weight. 
Instead of suspending the bar by a wire, it may be supported 
by small wheels at A and B. Y*e a square card or draftsman's 
triangle to test the right angles at p x , p 2 , and p 3 . 

10. Ex. 17. The apparatus of Ex. 13 may be used, with 
the addition of the lead strap. 

11. Ex. Is. The Author prefers to defer this experiment 
till the class is about to begin the study of sound. He takes 
it up in connection with a brief and informal study of the 
chapters on wave motion and simple Harmonic motion as given 
in the Mann & Twiss Physics, Chapters XIV and XV. Ex- 
cellent suspension clamps for pendulums are sold by apparatus 
dealers, but the slit cork answers admirably. 

12. Ex. 19. Cylindrical graduates of 250 cm. 3 capacity 
are best for this Exercise and are used in several others. These 
and nearly all glassware, thermometers, etc. may be bought 
very cheaply if imported duty free through the Bausch & 
Lomb ( Optical Company or any of the other well-known appar- 
atus dealers. 

Problem fa) The Hall pressure gauge IS sold by all t he dealers 
(price 75c). It shows the equality of pressures at a given 
depth perfectly but is of no use to prove quantitatively that 
the pressure is proportional to the depl h. 

13. Ex. 24. The 3-way *rla-> tube for thi- experiment iq 
more convenient than the usual V form it made as follows. 



226 APPENDICES 

Hold a T tube in a fish tail flame, the plane of the T being 
horizontal, and bend each of the three arms vertically down- 
ward. With this form the rubber tube extending to the 
mouth-piece will not "kink." The best dish for this experi- 
ment is cylindrical, the diameter being about 3 inches and the 
height 2 inches. See Bausch & Lomb's catalogue. 

14. Ex. 25. Blank hydrometers and paper millimeter 
scales may be had from the apparatus dealers. If the teacher 
prefer to shorten the exercise the tests may be made with a 
ready made hydrometer or lactometer. The Babcock cream 
test is easily made and if the school can afford the apparatus it 
will arouse much interest if given as an optional experiment. If 
the apparatus is ordered, ask for full directions to accompany it. 

15. Ex. 26. The operations of working glass and corks can 
best be shown to the students by the teacher. After being 
shown, one can learn only by practice. See Threlfall's Labora- 
tory Arts and Shenstone's Methods of Glass Blowing. 

16. Ex. 27. If the teacher wishes to make his own Boyle's 
Law Apparatus, he will find the form described in this ex- 
periment the easiest to make; and it works as well as any. 
The tubes fitted with the caps and screws may be obtained 
from The Central Scientific Co., Chicago, or the L. E. Knott 
Apparatus Co., Boston. 

17. Ex. 28. Paper scale thermometers, imported duty free, 
cost about 40c, but some of them are so inaccurate as to give 
very poor results. A much better thermometer, with the 
scale etched in the glass, costs about 90c. The boiler should 
have the water gauge and screw top, and may be made fairly 
tight if a rubber band is used for packing after the manner of 
a Mason fruit jar. If the boiler leaks, the pressure experi- 
ments will not succeed. The pressure gauge suggested by the 
Author is made from a thistle tube and a paper millimeter scale. 
The thistle top prevents the mercury from overflowing, and 
permits the gauge to act as a safety valve. 

18. Ex. 29. The Calorimeter of Exercise 30-32 is suitable for 
this experiment. 

19. Ex. 35 and 36. "Home made" telegraph instruments are 
easy to make. Many of the Author's students forge their 
levers and magnets from iron and mount them in hard wood 
bearings. The ingenuity of some boys if you get them started 



APPENDICES 



227 



is marvelous. They will make workable apparatus out of all 
kinds of junk. 

20. Ex. 38. This is regarded by the Author as one of the 
best experiments in the course. The coils furnished for this 
purpose by the dealers are expensive, but cheap substitutes that 
will work well are easily made. Wind the wire on a wooden 
reel, remove the one end of the reel, slip the coil off, and bind 
it all round with adhesive tape. The coils shown in Figs. 
138 and 139 of the Mann 6z Twiss Physics were made in this 
way and work satisfactorily. See Galvanometers and Shunts, 
Art. 21, below. 

21. Ex. 39. Galvanometers are of so many different pat- 
terns that it is useless to try to give instructions in a manual 
intended for general use. D'Arsonval's filling all the require- 
ments of this course and the Mann & Twiss Text may be 
bought from the Central Scientific Co., Chicago, and the L. E. 
Knott Apparatus Co., Boston, for about $6.00 each. Circulars 
giving full directions for setting up and reading the instruments, 
will be furnished with them if asked for. 

Shunts. — A strong current should never be sent through a 
sensitive galvanometer. In beginning an experiment, it is 
always best to shunt the galvanometer by connecting its 
two binding-posts across by means of a short wire, so that 
only a small fraction of the 
current goes through it. When 
the current is so small that the 
galvanometer is insensitive, a 
shunt of higher resistance may 
be used, or the shunt may be 
discarded. 

22. Ex.41. Scratch Brushes 
and other plater's materials 
may be bought from dealer- in 
plater's supplies. Fl °; ^-Commutator. The 

_ wires leading from the gal vanome- 

Commutator. In many ex- ter uIV in8erted at pii ^ (;<; all(1 

periments it is accessary thai those leading from the current cir- 
the current passing through cult at poets CC. 
the galvanometer l>e quickly reversed. Accordingly, a com- 
mutator, or reversing switch, is provided. A convenient and 
inexpensive device is shown in Fig. 53. 




228 APPENDICES 

The connections are made as shown, by wires dipping into 
holes containing mercury. To reverse the current through 
the galvanometer, lift the top, turn it through a right angle, 
and replace it. To break the current, leave off the cover. 

/^~X ^"~7\ /^~7\ When measuring current strength with 
VTJJ/ \}jj vjjy a galvanometer, or when standardizing 

I , Ba . — 1 & galvanometer with an electrolytic cell 

(copper voltameter), the connections 

should be made so that the current from 

x^r \ I -^ the battery may be reversed through 

(r wj Tu j, (^J the galvanometer, but not through the 

G V voltameter. In such a case the appara- 

Fig. 54. tus is arranged as in Fig. 54, in which G 

represents the galvanometer, Ba the battery, V the voltameter, 
and RB a resistance box for regulating the strength of the 
current. When an ammeter or volt-meter is being standardized, 
no commutator is needed, because these instruments read on 
one side of the zero only. 

The Copper Voltameter, Problem b. — This experiment re- 
quires a balance and weights that are accurate to a milligram. 
It is not recommended for the younger students. 

23. Renewing Exhausted Dry Cells. — Remove the paste- 
board cover, punch holes through the zinc walls, and place the cell 
in a jar of sal ammoniac solution. It will work as well as ever. 

24. Ex. 43. Instead of smoking the glass it may be painted 
with a thin paste made of whiting and alcohol. The alcohol 
evaporates, leaving a clean white coat which may be easily 
removed. 

25. Ex. 52. Instead of mirrors the glass plates of Ex. 54 
may be used. Screen off the light from the rear and use the 
reflection from the front surface. This avoids errors which 
result from refraction w T hen the light enters the glass and is 
reflected from the back surface. 

26. Ex. 57. This exercise is recommended for those schools 
where a good projection apparatus is not owned. The Author 
personally prefers to demonstrate these phenomena with the 
lantern, and also to place a spectroscope at the disposal of 
those students who wish to experiment themselves and may 
be trusted with it. A small direct vision spectroscope may be 
imported duty free from Germany for about $10.00. 



APPENDICES 



229 



G. PRESSURE AND TEMPERATURE OF WATER 
VAPOR 

This table gives the pressure P in millimeters of mercury 
of saturated water vapor at the temperature t° opposite 
which it appears. Any value of t° also represents the boiling 
point when the atmospheric pressure has the corresponding 
value of P. 



t 


P 


t 


P 


t 


P 


—5 


3.2 


17 


14.4 


75 


288.8 


—4 


3.4 


18 


15.3 


80 


354.9 


—3 


3.7 


19 


16.3 


85 


433.2 


2 


3.9 


20 


17.4 


90 


525.4 


—1 


4.2 


21 


18.5 


95 


633.6 





4.6 


22 


19.6 


96 


657.4 


1 


4.9 


23 


20.9 


97 


681.8 


2 


5.3 


24 


22.2 


98 


707.1 


3 


5.7 


25 


23.5 


98.2 


712.3 


4 


6.1 


26 


25.0 


98.4 


717.4 


5 


6.5 


27 


26.5 


98.6 


722.6 


6 


7.0 


28 


28.1 


98.8 


727.9 


7 


7.5 


29 


29.7 


99.0 


733.2 


8 


8.0 


30 


31.5 


99.2 


738.5 


9 


8.5 


35 


41.8 


99.4 


743.8 


10 


9.1 


40 


54.9 


99.6 


749.2 


11 


9.8 


45 


71.4 | 


99.8 


754.7 


12 


10.4 


50 


92.0 


100.0 


Y60.0 


13 


11 .1 


55 


117.5 


100. L> 


765.5 


14 


11.9 


60 


148.8 


100.4 


771.0 


15 


12.7 


65 


187.0 


100.6 


776.5 


1G 


13.5 


70 


233.1 


100.8 


782.1 










101.0 


787.7 



II. WAX. CEMENTS, SOLDERING 

1. Soft Wax, indispensable for temporarily sticking any- 
thing t o anyt hing else, is made by mell ing and si irring t ogel her 
40 part- of beeswax with 10 of Venice turpentine and l of 

rosin. When it is cold, cut it into sticks with a knife that has 

been dipped in gasoline, and wrap the sticks in paraffins 

paper and tinfoil. 

2. Beeswax axd Rosin Cement will stick almost any two 



230 APPENDICES 

materials together air tight. It is made by melting together 
equal parts of beeswax and rosin. It may be cast in a thin 
cake by using a paraffined pasteboard box cover as a mold. 
Use it as you would sealing wax. 

3. Cement for Joining Glass to Glass. — Boil 1 part of 
caustic potash with 3 of rosin, 5 of water, and 4 of plaster of 
Paris. 

4. Soldering. — Articles to be soldered must first be thor- 
oughly scraped clean, and be kept absolutely free from grease. 
The "soldering copper" should be kept clean and the tip covered 
with a bright coat of solder. It may be filed bright, heated, 
dipped in a strongly acid solution of chloride of zinc and then 
rubbed on a bar of solder. The chloride of zinc solution is 
made by dissolving sheet zinc scraps in hydrochloric acid, 
and is used as a flux on tin, lead, copper, or brass articles 
that are to be soldered. When used as a flux it need not 
be so strongly acid as when cleaning the soldering copper. 
Rosin is a good flux for iron and tin. The secret of success 
in soldering is to have the "copper" well tinned as above 
and hot (not red hot), and to have the article well cleaned 
and wet with the flux. Better have "two irons in the fire" 
so one will always be hot. 

A Gas Furnace for heating the soldering coppers is a great 
convenience and is inexpensive. 

Small articles may be conveniently soldered in a Bunsen 
flame, or with a mouth blowpipe. They must be held abso- 
lutely still until the melted solder has "set." 

For Soldering Galvanometer Suspensions, make a 
special "copper" from a small copper rod. Drill the upper 
end and tap in a piece of iron telegraph wire. Bend the upper 
end of this wire into a handle. 



I. REFERENCE BOOKS FOR TEACHERS 

Much information that is nearly indispensable to physics 
teachers may be found in any of the books of the following 
list: 

Elementary Practical Physics. Stewart & Gee. 3 vols. $4.85. 
The Macmillan Company. 



APPENDICES 231 

Physical Manipulation. Pickering. 2 vols. $7.00. Hough- 
ton, Mifflin & Co. 

Laboratory Arts. Threlfall. SI. 50. The Macmillan Company. 

The C. G. S. System of Units. Everett. SI. 25. The Mac- 
millan Company. 

Instructions to Voluntary Observers. U. S. Weather Bureau. 

The Barometer. U. S. Weather Bureau. 

Methods of Glass Blowing. Shenstone. SO. 80. Longmans 
& Co. 

Physical Measurements. Kolrausch. D. Applet on & Co. 

Physical Measurements. H. Whiting. 4 vols. D. C. Heath 
& Co. 

Experiences Elementaires de Physique. 2 vols. H. Abra- 
ham. Paris Gauthier-Villars. 



